Date of Award

Fall 2000

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

Denis L. Blackmore

Second Advisor

Amitabha Koshal Bose

Third Advisor

Victoria Booth

Fourth Advisor

Stanley S. Reisman

Fifth Advisor

John Tavantzis

Abstract

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.

Included in

Mathematics Commons

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