Process modeling and matlab

Process modeling and matlab

The Holling-Tanner model for predator-prey dynamics is given in a normalized form by the following 2 differential equations, where x represents the prey, and y the predator. The equations have 3 parameters; c, r, a that represent the characteristics of the individual species and the environment.

dx/dt=x(1-x) -cxy/(a+x)

dy/dt=ry(1-y/x)

In order to study this system, preform the following tasks. Use r=0.1, and a= 2/7:

  1. Calculate, and plot, the value of the non-trivial steady state solution (x>0, y>0) as a function of the parameter c.
  2. Simulate, and plot, the dynamic behavior of these equations (i.e. x vs. t, y vs. t)) for c=5 using a point very close to the steady state as the initial condition.
  3. Set c=6 and simulate, and plot, the dynamic behavior using the final state of the previous experiment as initial condition.
  4. Set c=7 and simulate, and plot, the dynamic behavior using the final state of the previous experiment as initial condition.
  5. Reset c=6 and simulate, and plot, the dynamic behavior using the final state of the previous experiment as initial condition.
  6. What do you observe? What general findings have you made about this system?

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