Adaptive Control and Synchronization of a Generalized Lotka-volterra System

The Lotka-Volterra equations are a system of equations proposed to provide a simplified model of twospecies predator-prey population dynamics. In this paper, we investigate the problem of adaptive chaos control and synchronization of a generalized Lotka-Volterra system discovered by Samardzija and Greller (1988). The Samardzija-Greller model is a two-predator, one-prey generalization of the Lotka-Volterra system. First, adaptive control laws are designed to stabilize the generalized Lotka-Volterra system to its unstable equilibrium point at the origin based on the adaptive control theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical generalized Lotka-Volterra systems with unknown parameters. Numerical simulations are shown to validate and demonstrate the effectiveness of the proposed adaptive control and synchronization schemes for the generalized Lotka-Volterra system.