No abstract

This paper proposes a stochastic three species food-chain model with harvesting and distributed delays. Some criteria for the global dynamics of all positive solutions, including the existence of global positive solutions, stochastic boundedness, extinction, global asymptotic stability in the mean, and the probability distribution, are established by using the stochastic integral inequalities, Lyapunov function method, and the inequality estimation technique. Furthermore, the effects of harvesting are discussed, the optimal harvesting strategy and the maximum of expectation of sustainable yield (MESY for short) are obtained. Finally, numerical examples are carried out to illustrate our main results.

We study a class of periodic general -species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the -species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature.

In this paper, a kind of fractional-order predator-prey (FOPP) model with a constant prey refuge and feedback control is considered. By analyzing characteristic equations, we carry out detailed discussion with respect to stability of equilibrium points of the considered FOPP model. Besides, the effects of prey refuge and feedback control are also studied by numerical analysis. Our study reveals that prey refuge and feedback control can be used to adjust the biomass of prey species and predator species such that prey species and predator species finally reach a better state level.

In this paper, we investigate the dynamical properties for a model of delay differential equations, which describes a virusimmune interaction in vivo. By analyzing corresponding characteristic equations, the local stability of the equilibria for infection-free, antibody-free, and antibody response and the existence of Hopf bifurcation with antibody response delay as a bifurcation parameter at the antibody-activated infection equilibrium are established, respectively. Global stability of the equilibria for infection-free, antibody-free, and antibody response, respectively, also are established by applying the Lyapunov functionals method. The numerical simulations are performed in order to illustrate the dynamical behavior of the model.