Analysis of discrete dynamical system models for competing species

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.

Name thesis:degree_name

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

Discipline thesis:degree_discipline

Mathematical Sciences

Year

2001

Author dc:creator

• Chen, Jerry J.

Contributors dc:contributor

• Denis L. Blackmore
• Amitabha Koshal Bose
• Victoria Booth

• Lotka-Volterra (LV) differential equations
• competing population species
• Exponentially Self-Regulating (ESR) population model
• Mathematics

Repository record dc:identifier

https://digitalcommons.njit.edu/dissertations/451

OAI identifier oai:identifier

oai:digitalcommons.njit.edu:dissertations-1506