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d) Suppose r1 = 0.4, r2 = 0.03, d =1,j =150,w = 300 .h = 1000 ,and k = 3000 . Find the equilibrium points
d) Suppose r1 = 0.4, r2 = 0.03, d =1,j =150,w = 300 .h = 1000 ,and k = 3000 . Find the equilibrium points of this system. You may do this with just algebra. or use a graphical method (nullclines). or use Sage or a graphing calculator. Note: There is one \"interesting" equilibrium point, that is not on either axis, i.e. for which N and P are both nonzero. e) With the parameters as in part (c) the trajectories approach a limit cycle attractor. Based on this, what can you say about the equilibrium point at which both N and P are nonzero? f) Now, using the same parameters as in part (c) but with r] = 0 ,2, nd the equilibrium points of the system again. By plotting a trajectory or some time series in Sage. what can you say this time about the equilibrium point at which both N and P are nonzero? What phenomenon has occurred between I]: 0.2 and r1: 0 ,4
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