#### Cannibalistic and Chaotic Flour Beetles

##### Andrew E Long

The parameters initially included reproduce the bifurcation results on p. 39 of Cushing's manuscript.

The tuning parameter is b, the birthrate.

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This is an example from Cushing's book An Introduction to Structured Population Dynamics.

The parameters initially included reproduce the bifurcation results on p. 39 of Cushing's manuscript.

The tuning parameter is b, the birthrate.

The parameters initially included reproduce the bifurcation results on p. 39 of Cushing's manuscript.

The tuning parameter is b, the birthrate.

- 1 year 8 months ago

This is an example I thought of after reading Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.

It's an SIR-type model, but one where the equilibrium (ws,wi,wr) is always the same, even as the weights in the transition matrix change.

It's an SIR-type model, but one where the equilibrium (ws,wi,wr) is always the same, even as the weights in the transition matrix change.

- 1 year 8 months ago

This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.

Galla age distribution model.

Thanks Mike! Interesting examples, as always....

Andy Long

Next up: an SIR.

Galla age distribution model.

Thanks Mike! Interesting examples, as always....

Andy Long

Next up: an SIR.

- 1 year 8 months ago

This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.

- 1 year 8 months ago

This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.

- 1 year 8 months ago

This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.

Next up: and SIR, and his interesting model of female birth weights.

Next up: and SIR, and his interesting model of female birth weights.

- 1 year 8 months ago

Thanks to

https://insightmaker.com/insight/25229/SIR-model-with-stochastic-events

https://insightmaker.com/insight/25229/SIR-model-with-stochastic-events

- 1 year 8 months ago

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

- 1 year 8 months ago

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

- 1 year 9 months ago

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

- 1 year 9 months ago

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

Experiment with adjusting the initial number of moose and wolves on the island.

Experiment with adjusting the initial number of moose and wolves on the island.

- 1 year 9 months ago

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale. It was "cloned" from a model that InsightMaker provides to its users, at

- 1 year 9 months ago

This is an example of an SIR (Susceptible, Infected, Recovered) model that has been re-parameterized down to the bare minimum, to illustrated the dynamics possible with the fewest number of parameters.

- 1 year 9 months ago

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

Experiment with adjusting the initial number of moose and wolves on the island.

Experiment with adjusting the initial number of moose and wolves on the island.

- 1 year 9 months ago

It seems that I've made a mess of mine! But it's a mess with a purpose....

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

Experiment with adjusting the initial number of moose and wolves on the island.

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

Experiment with adjusting the initial number of moose and wolves on the island.

- 1 year 9 months ago

This non-dimensionalized, sleekest most neatest model illustrates predator prey interactions using logistic growth for the moose population, for the wolf and moose populations on Isle Royale.

Thanks Scott Fortmann-Roe for the original model.

Thanks Scott Fortmann-Roe for the original model.

- 1 year 9 months ago

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale. It was "cloned" from a model that InsightMaker provides to its users, at

- 1 year 9 months ago

This is an example of an SIR (Susceptible, Infected, Recovered) model that has been re-parameterized down to the bare minimum, to illustrated the dynamics possible with the fewest number of parameters.

- 1 year 9 months ago

This is a simple example of (part of a) simple SIR (Susceptible, Infected, Recovered) model, suggested by De Vries, et al. in A Course in Mathematical Biology.

- 1 year 9 months ago

This is a first example of a simple SIR (Susceptible, Infected, Recovered) model.

- 1 year 9 months ago

This was cloned from

https://insightmaker.com/insight/32036/Lorentz-equations

Thanks!

The Lorenz equations can be tuned to produce chaotic dynamics. In this system, the sum of the three "stocks" (x, y, and z) is not conserved.

https://insightmaker.com/insight/32036/Lorentz-equations

Thanks!

The Lorenz equations can be tuned to produce chaotic dynamics. In this system, the sum of the three "stocks" (x, y, and z) is not conserved.

- 1 year 10 months ago

Thanks to

https://insightmaker.com/insight/1830/Rossler-Chaotic-Attractor

https://insightmaker.com/insight/1830/Rossler-Chaotic-Attractor

- 1 year 10 months ago

This simple model demonstrates logistic growth.The differential equation looks like

y'(t)=by(t)(1-y(t)/K)

where K is the carrying capacity of the quantity y.

y'(t)=by(t) - b/K*y(t)^2

so the loss term is of the form b/K.

y'(t)=by(t)(1-y(t)/K)

where K is the carrying capacity of the quantity y.

y'(t)=by(t) - b/K*y(t)^2

so the loss term is of the form b/K.

- 1 year 10 months ago

This simple model demonstrates exponential growth or decay in a population.

A comparable Mathematica file is at

http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/ExponentialGrowth-and-DecayModel.nb

A comparable Mathematica file is at

http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/ExponentialGrowth-and-DecayModel.nb

- 1 year 10 months ago