Dynamical properties of discrete Lotka-Volterra equations

A discrete version of the Lotka-Volterra differential equations for competing population species is analyzed in detail in much the same way as the discrete form of the logistic equation has been investigated as a source of bifurcation phenomena and chaotic dynamics. It is found that in addition to the logistic dynamics - ranging from very simple to manifestly chaotic regimes 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 certain parameter ranges.