Dynamical properties of discrete Lotka-Volterra equations

A discrete version of the Lotka-Volterra differential equations for competi ng population species is analyzed in detail in much the same way as the dis crete form of the logistic equation has been investigated as a source of bi furcation phenomena and chaotic dynamics. It is found that in addition to t he logistic dynamics - ranging from very simple to manifestly chaotic regim es in terms of governing parameters - the discrete Lotka-Volterra equations exhibit their own brands of bifurcation and chaos that are essentially two -dimensional in nature. In particular, it is shown that the system exhibits "twisted horseshoe" dynamics associated with a strange invariant set for c ertain parameter ranges. (C) 2001 Elsevier Science Ltd. All rights reserved .