Education | Insight Maker

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

charbel khachan

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 Ejemplo 9: Modelado de una Población v1

Gersain Galindez Buitron.

A visual look at using technology in school based on the article:

Levin, B. B., & Schrum, L. (2013). Using systems thinking to leverage technology for school improvement: Lessons learned from award-winning secondary Schools/Districts. Journal of Research on Technology in Education, 46(1), 29-51.

Clone of Using Systems thinking for technology in education

R B

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

Bechara Assouad

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

Yezabel Rincón

Crea un modelo del comportamiento básico de una población. Se modela las variables exógenas (Lluvias) que afectan el Alimento - Función No Lineal

Universidad del Cauca.

Profesor: Miguel Angel Niño Zambrano

curso: Enlace Curso en Moodle

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

Ejemplo 12: Modelado de una Población v4 -Función NoLineal

Miguel Angel Niño Zambrano

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

Prakash

Focus on verbal/linguistic and logical/mathematical intelligences robs us of the wealth untapped in the remaining six intelligences: interpersonal, intrapersonal, spacial, musical, naturalistic, and kinesthetic.

Howard Gardner's Theory of Multiple Intelligences (MI) proposes that cognition isn't unitary and that individuals cannot be described as having a single, quantifiable intelligence. Published in 1983, his theory stipulated seven of which one more was added a year later.

Note: Intelligence is defined as the ability to solve problems, the ability to create problems to be solved, and the ability to create a product or a service that is of value to one's culture.

The Lost Children

Quint Rahaman

This paints a broad picture for my non-profit of how tutoring helps disadvantaged youth and, with the right jump-start from a caring individual (R1 point), how learning can get learning and skill begets further skill. I appreciate any feedback to modifications because they might shape program direction.

Future iterations will show the low skilled isolated individual gets stuck in a cycle of "no-growth." I would also like to explore the dynamics of how the learner reduces dependence on the tutor.

Clone of How tutors help the learner causal loop

Col

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

Jun UMEDA

From HBR study, 2014; combined with Solow Growth Model, explains why business seeks technological solutions. Yet this is not sustainable, as there is a limit to the number of STEM-trained individuals to create technological solutions.

Clone of BridgingTheGap

Janet Simmons

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

Nick May

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

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

Supriyanto

Crea un modelo del comportamiento básico de una población. Se modela el Factor Limitativo por Alimento

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 10: Modelado de una Población v2 - Factor Limitativo

Gersain Galindez Buitron.

Clone of Clone of How many jobless graduates in the UK future scenarios

Maria Eryestin Nahak

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

Jay MJJ Gatsby

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

Ben Cope

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

Chiara Birk

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

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

Miguel Angel Niño Zambrano

10

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

JCU Environmental Biology

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

Maggie Schramm

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

Ben Cope

A visual look at using technology in school based on the article:

Levin, B. B., & Schrum, L. (2013). Using systems thinking to leverage technology for school improvement: Lessons learned from award-winning secondary Schools/Districts. Journal of Research on Technology in Education, 46(1), 29-51.

Clone of Using Systems thinking for technology in education

Divna Krpan

Education Models