Education | Insight Maker

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system. For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system. The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926). Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them. Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined. Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed. Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey. It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature. And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.

2. The food supply of the predator population depends entirely on the size of the prey population.

3. The rate of change of population is proportional to its size.

4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.

5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt = -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Clone of Clone of Predator-Prey Model ("Lotka'Volterra")

Francisco Marques

In this model I am trying to depict the multiple factors and interactions that impact student academic achievement. As educators, our goal is to optimize the progression of academic achievement, or as represented in this stock flow diagram maintain the stock (academic achievement) at the highest level. Multiple factors enhance achievement and, conversely, multiple factors interact to reduce the stock/rate of achievement. As individual teachers, we must understand the factors and relationships that increase and decrease achievement. In particular, teachers in training need to begin to build a mental model of these factors and relationships. Only then can we optimize our individual learning environments to ensure each child reaches his/her academic achievement potential.

Clone of Student Achievement

Te Kou Gage

The probability density function (PDF) of the normal distribution or Bell Curve of Normal or Gaussian Distribution is the mean or expectation of the distribution (and also its median and mode).

The parameter is its standard deviation with its variance then, A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.

However, those who enjoy upskirts are called deviants and have a variable distribution :)

A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.

If mu = 0 and sigma = 1

If the Higher Education Numbers Are Increased then the group decision making ability of society would be raised above that of a middle teenager as it is now

BUT

Governments can control children by using bad parenting techniques, pandering to the pleasure principle, so they will make higher education more and more difficult as they are doing

85% of the population has a qualification level equal or below a 12th grader, 17 year old ... the chance of finding someone with any sense is low (~1 in 6) and the outcome of them being chosen by those who are uneducated in the policies they are to decide is even more rare !!!

Experience means little if you don't have enough brain to analyse it

Democracy is only as good as the ability of the voters to FULLY understand the implications of the policies on which they vote., both context and the various perspectives. National voting of unqualified voters on specific policy issues is the sign of corrupt manipulation.

Democracy: Where a group allows the decision ability of a teenager to decide on a choice of mis-representatives who are unqualified to make judgement on social policies that affect the lives of millions.

The kind of children who would vote for King Kong who can hold a girl in one hand and swat fighter jets out of teh sky off the tallest building, doesn't have a brain cell or thought to call his own but has a nice smile and offers little girls sweets.

updated 16/3/2020 from 4 years 3 months ago

Clone of The probability density function (PDF) of the normal distribution or Bell Curve Gaussian Distribution by Guy Lakeman

Sebastian Franco

This qualitative model will describe the potential daily routine of one professional mathematics tutor tutoring at a 2 year college, and should include all elements of the environment in which tutoring takes place, how policies affect the tutor, how the tutor's daily routine contributes to overall student success in key areas, and how those contributions are consistent, or inconsistent, with the stated mission and goals of the college.

The model should include limitations/constraints that exist, and how those limitations effect other elements in the model.

Stage 1) Describe a skeleton model of the daily procedures a tutor would carry out on single day.

This current Model Contains a starting model of an individual human being in terms of generic Characteristics of majority of humans. This model contains elements like a brain, senses, ... etc. The brain part will be divided into functional brain regions including the limbic system, which has an impact on whether a particular behavior is reinforced and internalized, or suppressed. The limbic system is likely a major and relevant component in human learning, or the hindrance of student engagement with, and learning of, the material.

Clone of Clone of Math Lab Routine Model

Gary Schasteen

Crea un modelo del comportamiento básico de una población

Universidad del Cauca.

Profesor: Miguel Angel Niño Zambrano

curso: Enlace Curso en Moodle

Videos ejemplos: Enlace a la lista de videos del curso youtube

Clone of Clone of Ejemplo 11: Modelado de una Población_llevias

Luis Carlos Ruiz Chicangana

looking at the problem of teaching multi curriculum

Clone of Teaching Multi-curriculum

Cheryl

Model of speech recognition training for health care professionals.

Clone of Education simulation of five projects

Teemu Hyppänen

Ejemplo Básico de Retrasos de Material Nivel 3 - Cosechas Usando Funciones Históricas

Universidad del Cauca.

Profesor: Miguel Angel Niño Zambrano

curso: Enlace Curso en Moodle

Videos ejemplos: Enlace a la lista de videos del curso youtube

Clone of Clone of Ejemplo 7: Retraso de Material Nivel 3 Cosecha Usando Funciones Históricas

Cori RZ

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system. For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system. The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926). Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them. Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined. Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed. Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey. It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature. And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.

2. The food supply of the predator population depends entirely on the size of the prey population.

3. The rate of change of population is proportional to its size.

4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.

5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt = -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Clone of Predator-Prey Model ("Lotka'Volterra")

Caitlyn White

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system. For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system. The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926). Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them. Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined. Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed. Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey. It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature. And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.

2. The food supply of the predator population depends entirely on the size of the prey population.

3. The rate of change of population is proportional to its size.

4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.

5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt = -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Clone of Predator-Prey Model ("Lotka'Volterra")

Sebastian Mora

Scenario 3 CLD.

Scenario 3 5 November

Meredith Seaman

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system. For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system. The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926). Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them. Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined. Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed. Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey. It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature. And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.

2. The food supply of the predator population depends entirely on the size of the prey population.

3. The rate of change of population is proportional to its size.

4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.

5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt = -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Clone of Clone of Predator-Prey Model ("Lotka'Volterra")

Paulo C. Coimbra

Ejemplo Básico de Retrasos de Material Nivel 3 - Cosechas Usando Funciones Históricas

Universidad del Cauca.

Profesor: Miguel Angel Niño Zambrano

curso: Enlace Curso en Moodle

Videos ejemplos: Enlace a la lista de videos del curso youtube

Clone of Ejemplo 7: Retraso de Material Nivel 3 Cosecha Usando Funciones Históricas

David

ONE version of Success to the Successful in which equally productive persons/groups/processes gain shares of a per-period allocation of resources based on their respective performance. Differences in INITIAL allocation can lead to larger and larger gaps in performance and, therefore, next-period allocation.

Use to explore how initial inequality can exacerbate inequality. Adjust the "Gains" flow to explore how inequality itself can become a drag on overall productivity (will need additional primitives).

GSVS3559_Archetype_SuccessToSuccessful

Spencer Phillips

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system. For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system. The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926). Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them. Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined. Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed. Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey. It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature. And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.

2. The food supply of the predator population depends entirely on the size of the prey population.

3. The rate of change of population is proportional to its size.

4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.

5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt = -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Clone of Predator-Prey Model ("Lotka'Volterra")

Kenneth C

Z209 from Hartmut Bossel's System Zoo 1 p112-118. Compare with PCT Example IM-9010

Clone of Balancing an Inverted Pendulum

Pau Fonseca

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system. For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system. The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926). Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them. Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined. Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed. Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey. It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature. And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.

2. The food supply of the predator population depends entirely on the size of the prey population.

3. The rate of change of population is proportional to its size.

4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.

5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt = -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Clone of Predator-Prey Model ("Lotka'Volterra")

Vivian Velazco

Rotating Pendulum Z201 from System Zoo 1 p80-83

Clone of Rotating Pendulum

Ilandor@Ynev

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system. For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system. The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926). Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them. Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined. Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed. Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey. It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature. And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.

2. The food supply of the predator population depends entirely on the size of the prey population.

3. The rate of change of population is proportional to its size.

4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.

5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt = -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Clone of Predator-Prey Model ("Lotka'Volterra")

Rickard Westerbergh

In this model I am trying to depict the multiple factors and interactions that impact student academic achievement. As educators, our goal is to optimize the progression of academic achievement, or as represented in this stock flow diagram maintain the stock (academic achievement) at the highest level. Multiple factors enhance achievement and, conversely, multiple factors interact to reduce the stock/rate of achievement. As individual teachers, we must understand the factors and relationships that increase and decrease achievement. In particular, teachers in training need to begin to build a mental model of these factors and relationships. Only then can we optimize our individual learning environments to ensure each child reaches his/her academic achievement potential.

Clone of Student Achievement

Joseph F. Krupa

Problém zvyšujících se nároků studia

Studium VŠ

Irena Slanařová

Physical meaning of the equations

The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.

2. The food supply of the predator population depends entirely on the size of the prey population.

3. The rate of change of population is proportional to its size.

4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.

5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt = -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Clone of Prey&Predator

Hubi

Sistema de intervenção do Banco Central para regular a cotação do dólar. O sistema tem um loop que conduz naturalmente ao equilíbrio, isto é, a COTAÇÃO ATUAL tende, com o tempo, à COTAÇÃO DESEJADA pelo BC. Entretanto devido ao TEMPO DE REAÇÃO DO MERCADO, o sistema OSCILA mas ainda assim tende ao equilíbrio. Na verdade, o que faz a COTAÇÃO ATUAL oscilar, é a relação entre o TEMPO DE REAÇÃO DO MERCADO e o TEMPO DE AJUSTE da intervenção do BC. A frequência de oscilação é tanto maior quanto maior for a relação entre o TEMPO DE REAÇÃO DO MERCADO e o TEMPO DE AJUSTE do BC.

Dolar

Paulo Villela

Physical meaning of the equations

The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.

2. The food supply of the predator population depends entirely on the size of the prey population.

3. The rate of change of population is proportional to its size.

4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.

5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt = -

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Clone of Prey&Predator

Jonathan Federle

Education Models