Question f and g only

3. Consider the following toy predator-prey model: Dn+1=Dn+(1Dn)DnPnDn,Pn+1=PnaPn+bDnPn Here, Dn is the density of prey and Pn is the population of predator at time n. It says that in the absence of predator, the prey D grows logistically whereas the prey population declines. The predator kills off prey, and its consumption makes the predator grow. (a) Using Python, plot the first 100 generations of Dn and Pn with the following parameter values: a=0.5,b=1.2. with D0=0.1,P0=0.1. Also, output the value of D100 and P100 as well as the plot. (b) Repeat part (a) but with b=1.6. (c) Compute the steady states of the system (1) for general a,b. Verify that it is consistent with your answer in (a). (d) For general a,b write down a 2x2 matrix whose eigenvalues determine the stability of the system. (e) Compute the eigenvalues of this matrix for parameter values in (a) and in (b) (give their numerical values). Comment on whether these eigenvalues agree with the observed behaviour of the system for parts (a) and (b). (f) Suppose a=0.5By using part (d) (either using python or analytically) determine bo such that oscillations are observed if b>b0, but no oscillations are observed if b