WOLFRAM SYSTEM MODELER
GilpinGilpin population dynamics model |
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Diagram
Wolfram Language
In[1]:=
SystemModel["SystemDynamics.IntroductoryExamples.Gilpin"]
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Information
The Gilpin model is a model to describe and analyze the natural occurrence of chaotic motion in population dynamics.
References:
- Cellier, F.E. (1991), Continuous System Modeling, Springer-Verlag, New York, ISBN: 0-387-97502-0, 755p.
- Gilpin, M.E. (1979), "Spiral Chaos in a Predator-Prey Model," The American Naturalist, 113, pp.306-308.
Simulate the model across 5000 time units and plot the three populations:
You need to reduce the accuracy to 1e-10 in order for the simulation to run correctly.
Outputs (3)
| x1 |
Type: Real Description: Prey_1 population |
|---|---|
| x2 |
Type: Real Description: Prey_2 population |
| x3 |
Type: Real Description: Predator population |
Components (31)
 |
Source1 |
Type: Source Description: This is the (dummy) source model of System Dynamics |
|---|---|---|
 |
Prey_1 |
Type: Level Description: General System Dynamics level |
 |
Sink1 |
Type: Sink Description: This is the (dummy) sink model of System Dynamics |
|
Source2 |
Type: Source Description: This is the (dummy) source model of System Dynamics |
|
Prey_2 |
Type: Level Description: General System Dynamics level |
|
Sink2 |
Type: Sink Description: This is the (dummy) sink model of System Dynamics |
 |
Death_1 |
Type: Rate_3 Description: Unrestricted additive rate element with three influencing variables |
 |
Birth_2 |
Type: Rate_1 Description: Unrestricted rate element with one influencing variable |
|
Death_2 |
Type: Rate_3 Description: Unrestricted additive rate element with three influencing variables |
 |
Prod_3_1 |
Type: Prod_3 Description: Product of three influencing factors |
 |
k1 |
Type: Const Description: A constant factor |
|
Prod_3_2 |
Type: Prod_3 Description: Product of three influencing factors |
|
k2 |
Type: Const Description: A constant factor |
|
Prod_3_3 |
Type: Prod_3 Description: Product of three influencing factors |
|
k3 |
Type: Const Description: A constant factor |
|
Prod_3_4 |
Type: Prod_3 Description: Product of three influencing factors |
|
k4 |
Type: Const Description: A constant factor |
|
Predator |
Type: Level Description: General System Dynamics level |
|
Death_P |
Type: Rate_1 Description: Unrestricted rate element with one influencing variable |
 |
Birth_P |
Type: Rate_2 Description: Unrestricted additive rate element with two influencing variables |
|
Source3 |
Type: Source Description: This is the (dummy) source model of System Dynamics |
|
Sink3 |
Type: Sink Description: This is the (dummy) sink model of System Dynamics |
|
Prod_3_5 |
Type: Prod_3 Description: Product of three influencing factors |
|
k5 |
Type: Const Description: A constant factor |
|
Prod_3_6 |
Type: Prod_3 Description: Product of three influencing factors |
|
k6 |
Type: Const Description: A constant factor |
|
Prod_3_7 |
Type: Prod_3 Description: Product of three influencing factors |
|
k7 |
Type: Const Description: A constant factor |
|
Prod_3_8 |
Type: Prod_3 Description: Product of three influencing factors |
|
k8 |
Type: Const Description: A constant factor |
|
Birth_1 |
Type: Rate_1 Description: Unrestricted rate element with one influencing variable |