Consider the non-linear differential system
where a is a real parameter. Assume that a varies between the values -10 and 170.
Competing Species
Laboratory 4F
where a is a real parameter. Assume that a varies between the values -10 and 170.
Consider the non-linear differential system
1 Find all equilibrium points of the system. Their location and number will, of course, depend on a.
2 Classify the equilibrium points by linearization.
3 At what values of a does the number of equilibrium points change?
4 At what values of a does the ``type" of an equilibrium point change (e.g., from sink to saddle)?
5 The system models a situation, where two animal species compete for limited resources. x(t) and y(t) denote the sizes of the two animal populations at time t.
Explain, why the differential system above might be a reasonable model for such a situation. What is the meaning of the parameter a?
6 Can you make predictions about the long-term fate of the animal populations? How does the parameter a affect their fate?