#### Prey&Predator

##### Tsogbadrakh Banzragch

**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 becomesdx/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.

PredatorsThe 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.

- 3 years 8 months ago

#### Using Systems thinking for technology in education

##### Rob koch

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.

- 3 years 4 months ago

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

##### Guy Lakeman

**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 nowBUT 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

MATHS Statistics Physics Science Ecology Climate Weather Intelligence Education Probability Density Function Normal Bell Curve Gaussian Distribution Democracy Voting Politics Policy

- 1 year 3 months ago

#### Population Stock and Flow

##### Stephanie Krishnan

The birth fraction and life expectancy are variables and are set as per page 66 of the text. The population is the stock and the births and deaths are the flows.

- 6 years 4 weeks ago

#### orquesta

##### MARIA JESUS CAMINO

- 5 years 3 months ago

#### Predator-Prey Model ("Lotka'Volterra")

##### Jacek Chmielewski

**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 becomesdx/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.

PredatorsThe 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.

- 3 years 10 months ago

#### Balancing an Inverted Pendulum PCT Model

##### Geoff McDonnell ★

Perceptual Control Theory Model of Balancing an Inverted Pendulum. See Kennaway's slides on Robotics. as well as PCT example WIP notes. Compare with IM-1831 from Z209 from Hartmut Bossel's System Zoo 1 p112-118

- 7 years 9 months ago

#### The Educated Mind

##### Geoff McDonnell ★

Methods Education Learning Realist Understanding Explanation Knowledge

- 1 month 4 weeks ago

#### Population - BIDE

##### Todd Levine

- 8 years 4 months ago

#### Student Achievement

##### David Olsen

- 8 years 7 months ago

#### BridgingTheGap

##### Edythe ★

- 5 years 11 months ago

#### Fourier series

##### Tsogbadrakh Banzragch

The GIFs above show the 8-term Fourier series approximations of the square wave and the sawtooth wave.

- 4 years 1 month ago

#### The Modelling Process

##### Geoff McDonnell ★

Grimm's ODD and Nate Osgood's ABM Modeling Process and Courses See also Pattern Oriented Modelling IM-3834

Shaping Our Healthier Futures Health Care Education Methods Computation Concept Understanding Complexity

- 2 years 10 months ago

#### Bio103 Predator-Prey Model ("Lotka'Volterra")

##### John Petersen

**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 becomesdx/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.

PredatorsThe 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.

- 2 years 2 months ago

#### Startup University Model

##### Geoff McDonnell ★

Education University Health Care Capability Performance Workforce Organization

- 4 years 10 months ago

#### Version 10: Hattie Calibrated Education Scenario Tool Capability Demonstration

##### Robert L. Brown

*complex system*and a general call in the literature for causal models has been sounded. This modeling effort represents a strident first step in the development of an evidence-based causal hypothesis: an hypothesis that captures the widely acknowledged complex interactions and multitude of cited influencing factors. This non-piecemeal, causal, reflection of extant knowledge engages a neuro-cognitive definition of students. Through capture of complex dynamics, it enables comparison of different mixes of interventions to estimate net academic achievement impact for the lifetime of a single cohort of students. Results nominally capture counter-intuitive unintended consequences: consequences that too often render policy interventions effete. Results are indexed on Hattie Effect Sizes, but rely on research identified causal mechanisms for effect propagation. Note that the net causal interactions have been effectively captured in a very scoped and/or simplified format. Relative magnitudes of impact have been roughly adjusted to Hattie Ranking Standards (calibration): a non-causal evidence source.

**This is a demonstration model and seeks to exemplify content that would be engaged in a full or sufficient model development effort.**Budget & time constraints required significant simplifying assumptions. These assumptions mitigate both the completeness & accuracy of the outputs. Features serve to symbolize & illustrate the value and benefits of causal modeling as a performance tool.

- 3 months 3 weeks ago

#### Balancing an Inverted Pendulum

##### Geoff McDonnell ★

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

- 5 years 8 months ago

#### Launched at an Angle

##### Tsogbadrakh Banzragch

object is projected with an initial velocity u at an angle to the horizontal direction.

We assume that there is no air resistance .Also since the body first goes up and then comes down after reaching the highest point , we will use the Cartesian convention for signs of different physical quantities. The acceleration due to gravity 'g' will be negative as it acts downwards.

h=v_ox*t-g*t^2/2l=v_oy*t

- 4 years 1 month ago

#### Dynamic Models Learning Content

##### Geoff McDonnell ★

Learning THread for hybrid models including Grimm's ODD and Nate Osgood's ABM Modeling Process and Courses

- 2 years 4 months ago

#### Learning Levels by Bateson

##### Richard Turnock

- 2 years 7 months ago

#### Information Distribution Problem

##### Rayne Man

In this model, inputs balance with outputs creating a dynamic contribution.

- 7 months 1 week ago

#### S-Curve + Delay for Bell Curve by Guy Lakeman

##### Guy Lakeman

**S-Curve + Delay for Bell Curve Showing Erlang Distribution**

Generation of Bell Curve from Initial Market through Delay in Pickup of Customers

This provides the beginning of an Erlang distribution model

The **Erlang distribution** is a two parameter family of continuous probability distributions with support . The two parameters are:

- a positive integer '
**shape'** - a positive real '
**rate'**; sometimes the scale , the inverse of the rate is used.

MATHS Statistics Physics Science Ecology Climate Weather Intelligence Education Probability Density Function Normal Bell Curve Gaussian Distribution Democracy Voting Politics Policy Erlang

- 1 year 3 months ago

#### Velocity

##### Tsogbadrakh Banzragch

- 3 years 9 months ago

#### A Framework for K-12 Science Education

##### Geoff McDonnell ★

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas website

- 4 years 9 months ago