The dynamical behaviors of a two-species discrete ratio-dependent predator-prey sys- tem are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization meth...The dynamical behaviors of a two-species discrete ratio-dependent predator-prey sys- tem are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization method. Further, we also obtain a new sufficient condition to ensure that the positive equilibrium is globally asymptotically stable by using an iteration scheme and the comparison principle of difference equations, which generalizes what paper [G. Chen, Z. Teng and Z. Hu, Analysis of stability for a discrete ratio-dependent predator-prey system, Indian J. Pure Appl. Math. 42（1） （2011） 1-26] has done. The method given in this paper is new and very resultful comparing with papers [H. F. Huo and W. T. Li, Existence and global stability of periodic solutions of a discrete predator--prey system with delays, Appl. Math. Comput. 153 （2004） 337-351; X. Liao, S. Zhou and Y. Chen, On permanence and global stability in a general Gilpin- Ayala competition predator prey discrete system, Appl. Math. Comput. 190 （2007） 500-509] and it can also be applied to study the global asymptotic stability for general multiple species discrete population systems. At the end of this paper, we present an open question.展开更多
The combined effects of harvesting and time delay on predator-prey systems with Beddington-DeAngelis functional response are studied. The region of stability in model with harvesting of the predator, local stability o...The combined effects of harvesting and time delay on predator-prey systems with Beddington-DeAngelis functional response are studied. The region of stability in model with harvesting of the predator, local stability of equilibria and the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation due to the two-parameter geometric criteria developed by Ma, Feng and Lu [Discrete Contin. Dyn. Syst. Set B 9 （2008） 397-413]. The global stability of the positive equilibrium is inves- tigated by the comparison theorem. Furthermore, local stability of steady states and the existence of Hopf bifurcation for prey harvesting are also considered. Numerical simulations are given to illustrate our theoretical findings.展开更多
文摘The dynamical behaviors of a two-species discrete ratio-dependent predator-prey sys- tem are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization method. Further, we also obtain a new sufficient condition to ensure that the positive equilibrium is globally asymptotically stable by using an iteration scheme and the comparison principle of difference equations, which generalizes what paper [G. Chen, Z. Teng and Z. Hu, Analysis of stability for a discrete ratio-dependent predator-prey system, Indian J. Pure Appl. Math. 42（1） （2011） 1-26] has done. The method given in this paper is new and very resultful comparing with papers [H. F. Huo and W. T. Li, Existence and global stability of periodic solutions of a discrete predator--prey system with delays, Appl. Math. Comput. 153 （2004） 337-351; X. Liao, S. Zhou and Y. Chen, On permanence and global stability in a general Gilpin- Ayala competition predator prey discrete system, Appl. Math. Comput. 190 （2007） 500-509] and it can also be applied to study the global asymptotic stability for general multiple species discrete population systems. At the end of this paper, we present an open question.
文摘The combined effects of harvesting and time delay on predator-prey systems with Beddington-DeAngelis functional response are studied. The region of stability in model with harvesting of the predator, local stability of equilibria and the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation due to the two-parameter geometric criteria developed by Ma, Feng and Lu [Discrete Contin. Dyn. Syst. Set B 9 （2008） 397-413]. The global stability of the positive equilibrium is inves- tigated by the comparison theorem. Furthermore, local stability of steady states and the existence of Hopf bifurcation for prey harvesting are also considered. Numerical simulations are given to illustrate our theoretical findings.
