STABILITY ANALYSIS OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENT OF GENERALIZED TYPE USING LYAPUNOV FUNCTIONS

摘要

We consider a Lotka-Volterra type predator-prey model with piecewise constant arguments of generalized type and investigate the stability of the positive equilibrium point of the proposed model. Although the model includes piecewise constant delays, we do not use Lyapunov functionals. We establish the stability conditions by using Lyapunov functions of the corresponding model of ordinary differential equations. In order to illustrate the validity of our results, we present an appropriate example and numerical simulations.