Analysis of a delayed diffusive model with Beddington–DeAngelis functional response

Abstract

In this paper, a delayed diffusive phytoplankton-zooplankton model with Beddington–DeAngelis functional response and toxins is investigated. Existence of equilibria of the system are solved. The global asymptotic stability of the zooplankton-free equilibrium is obtained. The local stability of the coexistent equilibrium and existence of Hopf bifurcation are discussed. In addition, the properties of the Hopf bifurcation are studied based on the center manifold and normal form theory for partial differential equations. Finally, some numerical simulations are also carried out to confirm our theoretical analysis.

Influence of time delay on bifurcation of a synthetic drug transmission model with psychological addicts

“…On the other hand, there should be a period for a drug user in treatment before he relapses into the physiological addicts due to the effect of treatment and his self-control. With an eye to such considerations and motivated by the work of some other dynamical systems with time delay [26][27][28][29][30], we investigate a more realistic synthetic drugs transmission model as follows:…”

Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect

“…Of course, it also satisfies the need for humans to benefit from natural resources. The prey-predator systems with harvesting have been widely studied by a large number of scholars [13,[18][19][20][21][22][23]. Meng et al [19] studied a predator-prey system with harvesting prey and disease in prey species and found that the optimal harvesting effort is closely related to the incubation period of the infectious disease, and the maximum value of the optimal harvesting decreases with the increase of the time delay.…”

Dynamical analysis of a giving up smoking model with time delay

“…Yuan et al demonstrated that time delay can affect stability of a dynamical system and cause nonlinear phenomena such as Hopf bifurcation and periodic solutions [25,26]. For some other works about dynamical systems, one can refer to [27][28][29][30]. Therefore, it is very crucial to examine the effect of the time delay τ on system (1).…”