This paper is concerned with a diffusive Ivlev-type predator-prey system with Smith growth and a protection zone. By discussing the existence and non-existence of positive solutions,we discover that the incorporation ...This paper is concerned with a diffusive Ivlev-type predator-prey system with Smith growth and a protection zone. By discussing the existence and non-existence of positive solutions,we discover that the incorporation of the Smith growth function has enabled us to obtain a more precise criterion when judging the structure of bifurcation solutions, and determine a critical size for the protection zone. The results indicate that if the size of the protection zone is below the critical patch size, then the system has no positive steady state solution for excessively high intrinsic growth rates of predators. Conversely, if the size of the protection zone exceeds the critical patch size, there exists positive steady state solution regardless of how large the intrinsic growth rate of the predators is.展开更多
The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is considered.We discuss the existence and non-existence of positive steady state solutions by using the bifurcati...The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is considered.We discuss the existence and non-existence of positive steady state solutions by using the bifurcation theory.It is shown that the protection zone for prey has beneficial effects on the coexistence of the two species when the growth rate of predator is positive.Moreover,we examine the dependence of the coexistence region on the efficiency of the predator capture of the prey and the protection zone.展开更多
Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and ex...Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.展开更多
A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model, we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed ...A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model, we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed prey to predator in the Ivlev-type functional responses. The existence and uniqueness of the positive equilibrium of the model and the stability of the equilibrium of the model are studied under various conditions. Hopf bifurcation analysis of the delayed model is provided.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12161080)。
文摘This paper is concerned with a diffusive Ivlev-type predator-prey system with Smith growth and a protection zone. By discussing the existence and non-existence of positive solutions,we discover that the incorporation of the Smith growth function has enabled us to obtain a more precise criterion when judging the structure of bifurcation solutions, and determine a critical size for the protection zone. The results indicate that if the size of the protection zone is below the critical patch size, then the system has no positive steady state solution for excessively high intrinsic growth rates of predators. Conversely, if the size of the protection zone exceeds the critical patch size, there exists positive steady state solution regardless of how large the intrinsic growth rate of the predators is.
基金Supported by the National Natural Science Foundation of China(11761063).
文摘The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is considered.We discuss the existence and non-existence of positive steady state solutions by using the bifurcation theory.It is shown that the protection zone for prey has beneficial effects on the coexistence of the two species when the growth rate of predator is positive.Moreover,we examine the dependence of the coexistence region on the efficiency of the predator capture of the prey and the protection zone.
文摘Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.
基金Supported by the Anhui Provincial Department of National Land and Resources with their Science and Technology Project entitled "Research on a Dynamic Monitoring Land Usage,Evaluation and Decision Support Management System in Wanjiang Demonstration Area"(Grant No.2011-K-23)Anhui Agricultural University,China(Grant No.YJ2012-03,No.XK2013029 and No.11201002)The Natural Sciences and Engineering Research Council of Canada
文摘A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model, we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed prey to predator in the Ivlev-type functional responses. The existence and uniqueness of the positive equilibrium of the model and the stability of the equilibrium of the model are studied under various conditions. Hopf bifurcation analysis of the delayed model is provided.
