Differential Equations Problems
Problem 1:
Analyze the competing species model with the population of two species denoted by u and v.
u’=(a-bu)u—cuv,
Here a, b, c, p, q, and r are all positive parameters.
1. Recall and explain the meanings of these parameters;
2. Find all the equilibrium points. Point out which of them exists conditionally. Specify the condition(s) for the existence;
3. What is the general Jacobi matrix for the right-hand side functions.
4. Evaluate the Jacobi at each equilibrium. Calculate the eigenvalues of the Jacobi to decide the stability of each equilibrium.
5. Pick up a preferred equilibrium. Explain your reason for the choice.
