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1.
In this paper, we studied a diffusive predator-prey model with a functional response increasing in both predator and prey densities. The Turing instability and local stability are studied by analyzing the eigenvalue spectrum. Delay induced Hopf bifurcation is investigated by using time delay as bifurcation parameter. Some conditions for determining the property of Hopf bifurcation are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation. 相似文献
2.
In this paper, we study a delayed diffusive predator-prey model with fear effect and Holling II functional response. The stability of the positive equilibrium is investigated. We find that time delay can destabilize the stable equilibrium and induce Hopf bifurcation. Diffusion may lead to Turing instability and inhomogeneous periodic solutions. Through the theory of center manifold and normal form, some detailed formulas for determining the of Hopf bifurcation are presented. Some numerical simulations are also provided. 相似文献
3.
A diffusive predator-prey system with Holling functional response is considered. Firstly, existence of positive equilibrium of this reaction diffusion model under Neumann boundary condition is obtained. Meanwhile, the existence conditions for Turing instability and Hopf bifurcations of a system with Holling uppercaseexpandafter{romannumeral2} functional response are established. Next, the existence of the hydra effect is demonstrated, when the system is undergoing non-homogeneous steady-state solutions. Finally, numerical simulations are illustrated to support our theory results. 相似文献
4.
Guiquan Sun Shumin Liu Li Li Jing Li Zhen Jin 《Journal of Nonlinear Modeling and Analysis》2021,3(4):617-646
Mussel beds are important habitats and food sources for biodiversity in coastal ecosystems. The predation of mussel on algae depends not only on the current time and location, but also on the quantity of algae at other spatial location and time. To know the impacts of such predation behavior on the dynamics of mussel beds well, we pose a reaction-diffusion mussel-algae model coupling nonlocal interaction with kernel function. By calculating the critical conditions of Hopf bifurcation and Turing bifurcation, the conditions for the generation of Turing pattern are obtained. We find that the diffusion rate and predation rate of mussels have effect on the structure and density of spatial pattern of mussels under the nonlocal interaction, and the predation rate of mussels can produce different pattern types, while the diffusion rate plays a more important role on the pattern density. Moreover, the nonlocal interaction promotes the stability of the mussel beds. These results suggest that the nonlocal interaction between mussels and algaes is one of the important mechanisms for the formation of the spatial structure of mussel beds. 相似文献
5.
In this paper, we are concerned with the dynamics of a diffusive predator-prey model that incorporates the functional response concerning hunting cooperation. First, we investigate the stability of the semi-trivial steady state. Then, we investigate the influence of the diffusive rates on the stability of the positive constant steady state. It is shown that there exists diffusion-driven Turing instability when the diffusive rate of the predator is smaller than the critical value, which is dependent on the diffusive rate of the prey, and the semi-trivial steady state and the positive constant steady state are both locally asymptotically stable when the diffusive rate of the predator is larger than the critical value. Finally, the nonexistence of nonconstant steady states is discussed. 相似文献
6.
In order to understand the effect of the diffusion reaction on the interaction between tumor cells and immune cells, we establish a tumor-immune reaction diffusion model with homogeneous Neumann boundary conditions. Firstly, we investigate the existence condition and the stability condition of the coexistence equilibrium solution. Secondly, we obtain the sufficient and necessary conditions for the occurrence of Turing bifurcation and Hopf bifurcation. Thirdly, we perform some numerical simulations to illustrate the complex spatiotemporal patterns near the bifurcation curves. Finally, we explain spatiotemporal patterns in the diffusion action of tumor cells and immune cells. 相似文献
7.
Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response 总被引：1，自引：0，他引：1
Zhihua Liu 《Journal of Mathematical Analysis and Applications》2004,296(2):521-537
We consider a delayed predator-prey system with Beddington-DeAngelis functional response. The stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhães. An example is given and numerical simulations are performed to illustrate the obtained results. 相似文献
8.
Jia-Fang Zhang Wan-Tong Li Xiang-Ping Yan 《Applied mathematics and computation》2011,218(5):1883-1893
This paper is concerned with two-species spatial homogeneous and inhomogeneous predator-prey models with Beddington-DeAngelis functional response. For the spatial homogeneous model, the asymptotic behavior of the interior equilibrium and the existence of Hopf bifurcation of nonconstant periodic solutions surrounding the interior equilibrium are considered. Furthermore, the direction of Hopf bifurcation and the stability of bifurcated periodic solutions are investigated. For the model with no-flux boundary conditions, Turing instability of the interior equilibrium solution is studied. In particular, Turing instability region regarding the parameters is established. Finally, to verify our theoretical results, some numerical simulations are also included. 相似文献
9.
Shanshan ChenJunping Shi 《Journal of Differential Equations》2012,253(12):3440-3470
A reaction-diffusion model with logistic type growth, nonlocal delay effect and Dirichlet boundary condition is considered, and combined effect of the time delay and nonlocal spatial dispersal provides a more realistic way of modeling the complex spatiotemporal behavior. The stability of the positive spatially nonhomogeneous positive equilibrium and associated Hopf bifurcation are investigated for the case of near equilibrium bifurcation point and the case of spatially homogeneous dispersal kernel. 相似文献
10.
本文利用Schur—Cohn—Jury引理及分岔理论讨论了一类捕食与被捕食系统的动力学性质,分析了其正平衡点的稳定性,并讨论了Neimark—Sacker分岔稳定性与方向。通过数值模拟验证了所得结果的正确性。 相似文献
11.
在齐次Neumann边界条件下,研究一类自催化可逆三分子生化反应模型.首先对常微分系统,给出Hopf分支的存在性及稳定性.其次对偏微分系统,建立由扩散系数引起的Turing不稳定性,同时给出Hopf分支的存在性,并利用规范型理论和中心流形定理建立Hopf分支的方向和稳定性.最后,借助Matlab软件进行数值模拟,验证补... 相似文献
12.
Stability and bifurcation analysis of a delayed predator-prey model of prey dispersal in two-patch environments 总被引：1，自引：0，他引：1
In this paper, a class of delayed predator-prey model of prey dispersal in two-patch environments is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given. 相似文献
13.
Jia-Fang Zhang 《Applied Mathematical Modelling》2012,36(3):1219-1231
In this paper, a modified Holling-Tanner predator-prey model with time delay is considered. By regarding the delay as the bifurcation parameter, the local asymptotic stability of the positive equilibrium is investigated. Meanwhile, we find that the system can also undergo a Hopf bifurcation of nonconstant periodic solution at the positive equilibrium when the delay crosses through a sequence of critical values. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included. 相似文献
14.
In this paper, we investigate the stability and Hopf bifurcation of a diffusive predator-prey system with herd behaviour. The model is described by introducing both time delay and nonlocal prey intraspecific competition. Compared to the model without time delay, or without nonlocal competition, thanks to the together action of time delay and nonlocal competition, we prove that the first critical value of Hopf bifurcation may be homogenous or non-homogeneous. We also show that a double-Hopf bifurcation occurs at the intersection point of the homogenous and non-homogeneous Hopf bifurcation curves. Furthermore, by the computation of normal forms for the system near equilibria, we investigate the stability and direction of Hopf bifurcation. Numerical simulations also show that the spatially homogeneous and non-homogeneous periodic patters. 相似文献
15.
Maoxin Liao Xianhua TangChangjin Xu 《Communications in Nonlinear Science & Numerical Simulation》2012,17(1):183-194
In this paper, a three-species predator-prey system with two delays is investigated. By choosing the sum τ of two delays as a bifurcation parameter, we first show that Hopf bifurcation at the positive equilibrium of the system can occur as τ crosses some critical values. Second, we obtain the formulae determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included. 相似文献
16.
In this paper, a two-species predator-prey system with stage structure and harvesting is investigated. The existence of Hopf bifurcations of the system is given. And the stability and directions of Hopf bifurcations are determined by applying the normal form theory and the center manifold theorem. 相似文献
17.
This paper mainly studies the dynamic properties of the forest beetle outbreak model. The existence of the positive equilibrium point and the local stability of the positive equilibrium point of the system are analyzed, and the relevant conclusions are drawn. After that, the existence of Turing instability, Hopf bifurcation and Turing-Hopf bifurcation are discussed respectively, and the necessary conditions for existence are given. Finally, the normal form of the Turing-Hopf point is calculated, and some dynamic properties at the point are analyzed by numerical simulation. 相似文献
18.
Xuanliang Liu 《Applied mathematics and computation》2011,218(5):2300-2309
A predator-prey system with disease in the prey is considered. Assume that the incidence rate is nonlinear, we analyse the boundedness of solutions and local stability of equilibria, by using bifurcation methods and techniques, we study Bogdanov-Takens bifurcation near a boundary equilibrium, and obtain a saddle-node bifurcation curve, a Hopf bifurcation curve and a homoclinic bifurcation curve. The Hopf bifurcation and generalized Hopf bifurcation near the positive equilibrium is analyzed, one or two limit cycles is also discussed. 相似文献
19.
多时滞捕食-食饵系统正平衡点的稳定性及全局Hopf分支 总被引：1，自引：0，他引：1
本文首先用Cooke等人建立的关于超越函数的零点分布定理,研究了一类多时滞捕食-食饵系统正平衡点的稳定性及局部Hopf分支,在此基础上再结合吴建宏等人用等变拓扑度理论建立起的一般泛函微分方程的全局Hopf分支定理,进一步研究了该系统的全局Hopf分支. 相似文献
20.
In this paper, we studied a delayed host-generalist parasitoid model with Holling II functional response and diffusion term. The Turing instability and local stability are studied. The existence of Hopf bifurcation is investigated, and some explicit formulas for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived by the theory of center manifold and normal form method. Some numerical simulations are carried out. 相似文献