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NetLogo Models Library:
Sample Models/System Dynamics

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Wolf Sheep Predation (System Dynamics)

[screen shot]

If you download the NetLogo application, this model is included. (You can also run this model in your browser, but we don't recommend it; details here.)

## WHAT IS IT?

This is a model of a simple predator-prey ecosystem. It uses the System Dynamics Modeler to implement the Lotka-Volterra equations.

The Lotka-Volterra equations are a pair of first order, non-linear, differential equations that describe the dynamics of biological systems in which two species interact.

## HOW IT WORKS

At each step, the value of the SHEEP-BIRTHS flow is added to SHEEP stock, and the value of the SHEEP-DEATHS flow is subtracted from the SHEEP stock. The same is done for the WOLVES stock. Each flow is calculated in terms of the variables, and stocks that are linked to it.

## HOW TO USE IT

1. Press the SETUP button.
2. Press the GO button to run the model.
3. View the SHEEP and WOLVES monitors for the current value of those populations.
4. View the plot to observe the populations changing over time.

## THINGS TO NOTICE

What happens when the sheep population increases? And the wolves? Why do you think this is the case?

## THINGS TO TRY

Use the System Dynamics Modeler to change the values of the variables in the system, such as SHEEP-BIRTH-RATE and PREDATOR-EFFICIENCY.

## NETLOGO FEATURES

This model uses the System Dynamics Modeler to simulate the Lotka-Volterra equations.

## RELATED MODELS

Wolf-Sheep Predation
Wolf-Sheep Predation (docked)

## CREDITS AND REFERENCES

* Lotka, A.J. (1956). Elements of Mathematical Biology. New York: Dover.

* "Lotka-Volterra equation". From Wikipedia. http://en.wikipedia.org/wiki/Lotka-Volterra_equation

* Eric W. Weisstein. "Lotka-Volterra Equations." From MathWorld. http://mathworld.wolfram.com/Lotka-VolterraEquations.html

## HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

* Wilensky, U. (2005). NetLogo Wolf Sheep Predation (System Dynamics) model. http://ccl.northwestern.edu/netlogo/models/WolfSheepPredation(SystemDynamics). Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 2005 Uri Wilensky.

![CC BY-NC-SA 3.0](http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png)

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

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