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The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title: Analysis of discrete dynamical system models for competing species
Author: Chen, Jerry J.
View Online: njit-etd2001-052
(xi, 67 pages ~ 5.9 MB pdf)
Department: Department of Mathematical Sciences
Degree: Doctor of Philosophy
Program: Mathematical Sciences
Document Type: Dissertation
Advisory Committee: Blackmore, Denis L. (Committee chair)
Bose, Amitabha Koshal (Committee member)
Booty, Michael R. (Committee member)
Reisman, Stanley S. (Committee member)
Tavantzis, John (Committee member)
Date: 2001-01
Keywords: Lotka-Volterra (LV) differential equations
competing population species
Exponentially Self-Regulating (ESR) population model
Availability: Unrestricted

A discrete version of the Lotka-Volterra (LV) differential equations for competing population species is analyzed in detail, much the same way as the discrete form of the logistic equation has been investigated as a source of bifurcation phenomena and chaotic dynamics. Another related system, namely, the Exponentially Self Regulating (ESR) population model, is also thoroughly analyzed. It is found that in addition to logistic dynamics - ranging from the very simple to manifestly chaotic regimes in terms of the governing parameters - the discrete LV model and the ESR model exhibit their own brands of bifurcation and chaos that are essentially two dimensional in nature. In particular, it is shown that both systems exhibit "twisted horseshoe" dynamics associated to a strange invariant set for certain parameter ranges.

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