Question

# consider the following systems of rate of change equations system A : dx/dt=3x(1-x/10)-1/20xy , dy/dt=-5y+xy/20, system...

consider the following systems of rate of change equations system A : dx/dt=3x(1-x/10)-1/20xy , dy/dt=-5y+xy/20, system B: dx/dt=3x-xy/100, dy/dt=15y(1-y/17)+25xy. in both of these systems,x and y refer to the number of two different species at time t.In particular, in one of these systems, the prey is large animals and the predators are small animals, such as piranhas and humans. Thus it takes many predators to eat one prey, but each prey eaten is a tremendous benefit for the predator population. The other system has very large predators and very small prey.(a) For both systems of differential equations, what does x represent? the predator or the prey? explain. (b) what system represents predator and prey that are relatively the same size? explain. (c) for the system (a0 plot all nullclines and use this plot to determine all equilibrium solutions, verify your equilibrium solutions algebraically

The solution is as follows

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