The Lotka-Volterra equations described in Sec. 28.2 have been refined to include additional factors that impact predator-prey dynamics. For example, over and above predation, prey population can be limited by other factors such as space. Space limitation can be incorporated into the model as a carrying capacity (recall the logistic model described in Prob. 28.16) as in

Where K = the carrying capacity. Use the same parameter values and initial conditions as in Sec. 28.2 to integrate these equations from t 5 0 to 100 using ode45.
(a) Employ a very large value of K = 108 to validate that you obtain the same results as in Sec. 28.2.
(b) Compare (a) with the more realistic carrying capacity of K = 200. Discuss your results.

Transcribed Image Text:

-희x_bry dx dt dy -=-cy + dry dt