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Question: 1 let p be a fixed point of a nonlinear...

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1. Let p be a fixed point of a nonlinear map f. Given an0, find a geometric condition on f under which all points in N (p) are in the basin of p. Use cobweb plot analysis to explain your reasoning. Hint: By geometric condition, I mean some constraint on f and/or f in the neighborhood of p. One example condition that you can improve upon: Vr (p- e,p),f(r) >& f(x)<p Vr E (p,p+e),f(x) < & f(x) > p In more words and less notation: provided f(x) remains between the lines y r and y p in the epsilon neighborhood of p, all points in the neighborhood are in the basin of p. This question is deeper than you may think at first, and showing your condition works for a single example is not proving that it works for all example functions f. Your condition needs to work for all f.
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