Document Type
Dissertation
Date of Award
Fall 1-31-2001
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.
Recommended Citation
Chen, Jerry J., "Analysis of discrete dynamical system models for competing species" (2001). Dissertations. 451.
https://digitalcommons.njit.edu/dissertations/451
