A New Chaotic Lotka-Volterra Population Biology System, Its Dynamic Analysis, and FPGA Implementation

Abstract

In mathematical ecology, Lotka-Volterra population biology models describe dynamical systems showing the nonlinear interaction between predator and prey population species. Eilersen et al. [4] examined the Lotka-Volterra model of a population biology system consisting of one predator and two prey population species of which one prey is affected by a disease. Eilersen et al. [4] observed chaos in the Lotka-Volterra ecological model when the disease is contagious enough to keep going and spread over the affected prey species. A new chaotic Lotka-Volterra ecological disease model is derived in this work by adding a self-interacting nonlinear term for the infected prey species in the Eilersen chaotic disease model [4]. We show that the new chaotic Lotka-Volterra ecological disease model has two unstable rest points and a stable focus rest point. We conduct a detailed bifurcation analysis for the new Lotka-Volterra population biology model. We demonstrate that the new chaotic model exhibits multi-stability properties. Finally, we design an experimental FPGA model for the implementation of the proposed chaotic Lotka-Volterra population biology model.