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, 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
We propose an epidemic model consisting five compartments within a total population with Crowley-Martin incidence rate and Holling type Ⅱ treatment,where total population is separated by the susceptible, the vaccinat...We propose an epidemic model consisting five compartments within a total population with Crowley-Martin incidence rate and Holling type Ⅱ treatment,where total population is separated by the susceptible, the vaccinated, the exposed, the infected and the removed in this paper. We firstly prove that the epidemic model admits a unique global positive solution by contradiction. We then find out that diseases tend to extinction provided that the basic reproduction number is less than one. Moreover, the sufficient conditions of persistence for infectious diseases are obtained by constructing suitable Lyapunov functions.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 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].
基金supported by NSFC under grants 11201075 and 11601085。
文摘We propose an epidemic model consisting five compartments within a total population with Crowley-Martin incidence rate and Holling type Ⅱ treatment,where total population is separated by the susceptible, the vaccinated, the exposed, the infected and the removed in this paper. We firstly prove that the epidemic model admits a unique global positive solution by contradiction. We then find out that diseases tend to extinction provided that the basic reproduction number is less than one. Moreover, the sufficient conditions of persistence for infectious diseases are obtained by constructing suitable Lyapunov functions.
