The model of global species

  1. (30 marks) Consider the model of gungeabg species: dx = ax(1 — x) — bxy dt dy di = cy(1 — y) — dxy a. Find all the stationary points. b. Choose parameters a, b, c and d that ensure the species can coexist, then draw local phase portraits near the stationary points and a global phase portrait for your choice of parameters. Pay attention to the behaviour on the nullclines and near eigenvectors. c. Choose parameters a, b, c and d for which only one of the species can survive, then draw local phase portraits near the stationary points and a global phase portrait for your choice of parameters. Pay attention to the behaviour on the nullclines and near eigenvectors. d. Choose parameters a, b, c and d and an initial condition and plot x(t) and y(t). Describe the behaviour of x and y in words. 2. Provide a written summary of the case study you have been working on. Your summary should include: a. (10 marks) A description of the problem and the mathematical model. b. (20 marks) An analysis of the model. c. (30 marks) A discussion of the limitations of the model, a suggestion for a modification and an analysis of the modified model. ti