The qualitative behavior of solutions for a generalized Gause type predator prey system was studied.A large number of biological and bioeconomic models are special cases of this system.The system was investigated in t...The qualitative behavior of solutions for a generalized Gause type predator prey system was studied.A large number of biological and bioeconomic models are special cases of this system.The system was investigated in the region D={(x,y)|x>0,y>0} because of the biological meaning of the system.The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system,which ensure that the system has at least one limit cycle.The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare Bendixson are efficiently employed in the research.The main results and their consequences presented not only generalize some known results,but also improve some corresponding results of other authors.展开更多
A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By...A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By analyzing the corresponding characteristic equations,the local stability of each of the nonnegative equilibria is discussed.The existence of Hopf bifurcations at the positive equilibrium is established.By using Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions are obtained for the global stability of the positive equilibrium,the nonnegative boundary equilibrium and the trivial equilibrium of the model,respectively.Numerical simulations are carried out to illustrate the main results.展开更多
文摘The qualitative behavior of solutions for a generalized Gause type predator prey system was studied.A large number of biological and bioeconomic models are special cases of this system.The system was investigated in the region D={(x,y)|x>0,y>0} because of the biological meaning of the system.The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system,which ensure that the system has at least one limit cycle.The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare Bendixson are efficiently employed in the research.The main results and their consequences presented not only generalize some known results,but also improve some corresponding results of other authors.
基金Supported by the Social Science Foundation of Hebei Province(HB23TJO03)。
文摘A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By analyzing the corresponding characteristic equations,the local stability of each of the nonnegative equilibria is discussed.The existence of Hopf bifurcations at the positive equilibrium is established.By using Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions are obtained for the global stability of the positive equilibrium,the nonnegative boundary equilibrium and the trivial equilibrium of the model,respectively.Numerical simulations are carried out to illustrate the main results.
