Journal of Computations & Modelling

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

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• 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 (𝑦1, 𝑦2) 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.