MAT 1300 Lecture 5: MAT1330 discrete-time dynamical systems
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MAT 1300 Full Course Notes
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Cobwebbing (cid:73) suppose we have a discrete time dynamical system (cid:73) go horizontal to the diagonal line, then vertical to f (xt). If we"re nearby, we may move closer or farther away. If we are exactly on the point, then there is no change. A point x is an equilibrium of xt+1 = f (xt) if f (x ) = x . In the gures below, there is 1 equilibrium, 3 equilibria, and no equilibria. Since f (x ) = x , we can use this to solve for equilibria. 0 = 2a a = 0 is the only equilibrium. 0 = x (x 1) x = 0 or 1. Homework: find the equilibria for xt+1 = 1. However, one of these is not biologically meaningful. Be careful: if you write down answers that are biologically meaningless when the question refers to biology, you"ll lose marks.
