Stability and Boundedness Analysis of Lotka-Volterra Prey-Predator Model with Prey Refuge and Predator Cannibalism

Abstract

Abstract In this paper, a prey-predator system incorporating prey refuge and predator cannibalism is studied. The stability and ultimate boundedness of the analyzed state parameters (y_1,y_2) defining the system are obtained using the Lyapunov’s second or direct method. We construct a suitable complete Lyapunov function for the nonlinear system and demonstrate its efficacy. The method is built upon applying various theoretical Lyapunov functions. By constructing a Lyapunov function which possesses a functional relationship to the the original model system, we give sufficient conditions which ensure the stability and ultimate boundedness of the state parameters describing the nonlinear prey-predator system. We give a numeric example to illustrate the result obtained. JEL classification numbers: 34C27, 34D23, 34C25. Keywords: Prey-predator system, Prey refuge, Predator cannibalism, Stability, Boundedness, Lyapunov’s method.