In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term....In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.展开更多
In this paper,a class of predator-prey model with Crowley-Martin type functional response and time delay is considered.By choosing the delay as a bifurcation parameter,it is shown that Hopf bifurcation occurs as the d...In this paper,a class of predator-prey model with Crowley-Martin type functional response and time delay is considered.By choosing the delay as a bifurcation parameter,it is shown that Hopf bifurcation occurs as the delay passes through a certain critical value.Some numerical simulations for verifying the main results are also provided.展开更多
In this paper, an HIV dynamics model with two distributed intracellular delays incorporating Crowley-Martin functional response infection rate is investigated. The authors take into account multiple stage disease tran...In this paper, an HIV dynamics model with two distributed intracellular delays incorporating Crowley-Martin functional response infection rate is investigated. The authors take into account multiple stage disease transmission and the latently infected cells（not yet producing virus） in our system. The authors consider nonnegativity, boundedness of solutions, and global asymptotic stability of the system. By constructing suitable Lyapunov functionals and using the Lyapunov-La Salle invariance principle, the authors prove the global stability of the infected（endemic） equilibrium and the diseasefree equilibrium for time delays. The authors have proven that if the basic reproduction number R_0 is less than unity, then the disease-free equilibrium is globally asymptotically stable, and if R_0 is greater than unity, then the infected equilibrium is globally asymptotically stable. The results obtained show that the global dynamic behaviors of the model are completely determined by the basic reproduction number R_0 and that the time delay does not affect the global asymptotic properties of the model.展开更多
In this paper, we investigated an impulsive predator-prey model with mu- tual interference and Crowley-Martin response function. By the comparison theorem and the analysis technique of [12,14], sufficient conditions f...In this paper, we investigated an impulsive predator-prey model with mu- tual interference and Crowley-Martin response function. By the comparison theorem and the analysis technique of [12,14], sufficient conditions for the per-manence of the impulsive model are obtained, which generalizes one of main results of [4].展开更多
文摘In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.
文摘In this paper,a class of predator-prey model with Crowley-Martin type functional response and time delay is considered.By choosing the delay as a bifurcation parameter,it is shown that Hopf bifurcation occurs as the delay passes through a certain critical value.Some numerical simulations for verifying the main results are also provided.
基金supported partially by Scientific Research Staring Foundation,Henan Normal University(qd13045)
文摘In this paper, an HIV dynamics model with two distributed intracellular delays incorporating Crowley-Martin functional response infection rate is investigated. The authors take into account multiple stage disease transmission and the latently infected cells（not yet producing virus） in our system. The authors consider nonnegativity, boundedness of solutions, and global asymptotic stability of the system. By constructing suitable Lyapunov functionals and using the Lyapunov-La Salle invariance principle, the authors prove the global stability of the infected（endemic） equilibrium and the diseasefree equilibrium for time delays. The authors have proven that if the basic reproduction number R_0 is less than unity, then the disease-free equilibrium is globally asymptotically stable, and if R_0 is greater than unity, then the infected equilibrium is globally asymptotically stable. The results obtained show that the global dynamic behaviors of the model are completely determined by the basic reproduction number R_0 and that the time delay does not affect the global asymptotic properties of the model.
基金supported by the Natural Science Foundation of Fujian Province(2015J01012,2015J01019,2015J05006)the Scientific Research Foundation of Fuzhou University(XRC-1438)
文摘In this paper, we investigated an impulsive predator-prey model with mu- tual interference and Crowley-Martin response function. By the comparison theorem and the analysis technique of [12,14], sufficient conditions for the per-manence of the impulsive model are obtained, which generalizes one of main results of [4].
