A class of virus dynamics model with intracellular delay and nonlinear infection rate of Beddington-DeAngelis functional response is analysed in this paper. By constructing suitable Lyapunov functionals and using LaSalle type theorem for delay differential equations, we show that the global stability of the infection-free equilibrium and the infected equilibrium depends on the basic reproductiv...

A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and themethod of successor function, we obtain the systemwith impulsive effects that has an order o...

In this paper we study a two-consumers-one-resource competing system with Beddington-DeAngelis functional response. The two consumers competing for a renewable resource have intraspecific competition among their own populations. Firstly we investigate the extinction and uniform persistence of the predators, local and global stability of the equilibria, and existence of Hopf bifurcation at the p...

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results. Copyright q 2008 Can-Yun Huang et al. This is an open acce...

A delayed three-species food chain system with two types of functional responses, Holling type and Beddington–DeAngelis type, is investigated. By analyzing the distribution of the roots of the associated characteristic equation, we get the sufficient conditions for the stability of the positive equilibrium and the existence of Hopf bifurcation. In particular, the properties of Hopf bifurcation ...

We consider a Leslie-Gower model with the Beddington-DeAngelis functional response, Allee effect, and Caputo fractional order derivative. first establish existence, uniqueness, non-negativity, boundedness of solutions to confirm biological feasibility model. Moreover, Lyapunov direct method including generalized LaSalle invariance principle is applied investigate global stability prey-free poin...

In this paper, we investigate the emergence of a predator-prey model with Beddington-DeAngelistype functional response and reaction-diffusion. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. Based on the stability and bifurcation analysis, we give the spatial pattern formation via numerical simulation, i.e., the evolution process of the model near the coexistence...