Answer Happy

1. Consider a model for the dynamics of two interacting species given by the following system of ordinary differential equations du = a (b + 1) + u'v, dr du = bu-u'u, d! u(0) = "">0, (0) = 0° > 0, where a, b,y > 0 are strictly positive constants. (a) Determine the type of interaction between the species, i.e., is the system competit- ive, mutualistic or predator-prey (note this may vary depending on the population size). You may assume without proof that the size of the populations remain strictly positive for all times. (b) Determine the unique strictly positive steady state of the system. (c) Show that the steady state above is linearly asymptotically stable if and only if a' >(y-1)-1. [4 marks) [1 marks) [5 marks)