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:
- Calculate, and plot, the value of the non-trivial steady state solution (x>0, y>0) as a function of the parameter c.
- 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.
- Set c=6 and simulate, and plot, the dynamic behavior using the final state of the previous experiment as initial condition.
- Set c=7 and simulate, and plot, the dynamic behavior using the final state of the previous experiment as initial condition.
- Reset c=6 and simulate, and plot, the dynamic behavior using the final state of the previous experiment as initial condition.
- What do you observe? What general findings have you made about this system?
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