Chaotic Coexistence in a Top-predator Mediated Competitive Exclusive web |
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| Authors: | Brian ?Bockelman Email author" target="_blank">Bo?DengEmail author Elizabeth?Green Gwendolen?Hines Leslie?Lippitt Jason? Sherman |
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| Institution: | (1) Department of Mathematics, State University of West Georgia, Carrollton, GA USA, 30118;(2) Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, NE USA, 68588-0323;(3) Department of Mathematics, California State University at Fullerton/Iowa State University, Ames, IA USA, 50011;(4) Department of Mathematics, Kent State University, Kent, OH USA, 44240 |
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| Abstract: | A basic food web of 4 species is considered, of which there is a bottom prey X, two predators Y, Z on X, and a top predatorW only on Y. The study concerns with how one type of chaotic coexistence arises. It is shown that under the situation that without the top-predator W, competitor Z goes to extinction, without Z the XYW locks in a periodic cycle, yet with all species, the noncompetitiveZ can derive the dynamics from periodic orbits to chaos. The dynamics can be captured analytically by 1-dimensional unimodal and multimodal maps and symbolic shift maps.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th
birthday. |
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