In the predator-prey model in Equation 50.2, let a = 1, c = 0.1, k = 1, lambda = 0.1. (By hand) Determine the equilibrium points.
Conduct an analysis of the stability of the equilibrium points and sketch the solutions (We did this in class) (MATLAB) Use MATLAB to plot the phase portrait and the direction field. (MATLAB)
Suppose the number of shark in the water are deterring tourism (surfing, scuba diving etc) and the authorities want to reduce the shark population by culling one or both the species.
How should they proceed? You can answer this by studying the behavior of the system for varying initial conditions.
Read Section 52. (MATLAB) Estimate the period of oscillation. (MATLAB) Now simulate equations 50.1.
Use b = 0.02 and the rest of the constants as above. How does the answer differ from the one above?