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Global behaviour of a predator-prey like model with piecewise constant arguments
1a Department of Mathematics , Faculty of Education, Nevsehir Haci Bektas Veli University , Nevsehir 50300 , Turkey.
Abstract:
The present study deals with the analysis of a predator-prey like model consisting of system of differential equations with piecewise constant arguments. A solution of the system with piecewise constant arguments leads to a system of difference equations which is examined to study boundedness, local and global asymptotic behaviour of the positive solutions. Using Schur-Cohn criterion and a Lyapunov function, we derive sufficient conditions under which the positive equilibrium point is local and global asymptotically stable. Moreover, we show numerically that periodic solutions arise as a consequence of Neimark-Sacker bifurcation of a limit cycle.
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