The Lotka-Volterra Model for Competition Controlled by a Sliding Mode Approach

This paper deals with a variation of the Lotka-Volterra model and its control using Sliding Mode Control (SMC). The Lotka-Volterra model consists of two nonlinear equations of the equilibrium region, where they are calculated and their local stability analysis and a design of a controller are conducted using the Lyapunov approach. After that, this paper presents the system’s control in asymptotical stable and unstable regions. The proposed control strategy is an SMC strategy, which in fact is robust for parameter variations and disturbances. Often, the Lotka-Volterra model parameters are difficult to be identified or they are identified with large uncertainties because they can change over time. Simulation results are shown to demonstrate the proposed control strategy performance.