Lotka-Volterra Population Dynamics
Lotka-Volterra Population Dynamics
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This notebook generates phase portraits for a simple model of sheep-rabbit competition. Rabbits are represented by x. Sheep by y.
System of equations
System of equations
Calculate fixed points
Calculate fixed points
Linearized version
Linearized version
Linearize
Linearize
Classification of each fixed point
Classification of each fixed point
Phase portraits with eigenvectors
Phase portraits with eigenvectors
Make a table of eigenvectors, eigenvalues, etc.
Make a table of eigenvectors, eigenvalues, etc.
Nonlinear version
Nonlinear version
Full phase portrait
Full phase portrait
Zoomed-in phase portraits
Zoomed-in phase portraits
Near (6,0)
Near (6,0)
Near (0,2)
Near (0,2)
Near (0,0)
Near (0,0)
Near the saddle point
Near the saddle point