title: Global behaviour of a predator-prey like model with piecewise constant arguments.
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.
authors.affiliation: a Department of Mathematics , Faculty of Education, Nevsehir Haci Bektas Veli University , Nevsehir 50300 , Turkey.
authors.forename: Senol
authors.initials: S
authors.lastname: Kartal
authors.forename: Fuat
authors.initials: F
authors.lastname: Gurcan
mesh_terms: D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior
keywords: 39A10; 39A28; 39A30; bifurcation; difference equation; piecewise constant arguments; stability