Dynamics of Bacterial white spot disease spreads in Litopenaeus Vannamei with time-varying delay.

In this paper, we mainly consider a eco-epidemiological predator-prey system where delay is time-varying to study the transmission dynamics of Bacterial white spot disease in Litopenaeus Vannamei, which will contribute to the sustainable development of shrimp. First, the permanence and the positiveness of solutions are given. Then, the conditions for the local asymptotic stability of the equilibriums are established.

Dynamical behaviour of an intraguild predator-prey model with prey refuge and hunting cooperation.

An intraguild predator-prey model including prey refuge and hunting cooperation is investigated in this paper. First, for the corresponding ordinary differential equation model, the existence and stability of all equilibria are given, and the existence of Hopf bifurcation, direction and stability of bifurcating periodic solutions are investigated. Then, for partial differential equation model, the diffusion-driven Turing instability is obtained.

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

In this paper, a delayed diffusive predator-prey model with schooling behaviour and Allee effect is investigated. The existence and local stability of equilibria of model without time delay and diffusion are given. Regarding the conversion rate as bifurcation parameter, Hopf bifurcation of diffusive system without time delay is obtained.

The impact of media on the spatiotemporal pattern dynamics of a reaction-diffusion epidemic model.

In this paper, a reaction-diffusion SI epidemic model with media impact is considered. The boundedness of system and the existence of the state are given. The local stabilities of the endemic states are analyzed.

Stability and Hopf bifurcation analysis of a delayed phytoplankton-zooplankton model with Allee effect and linear harvesting.

In this article, a delayed phytoplankton-zooplankton system with Allee effect and linear harvesting is proposed, where phytoplankton species protects themselves from zooplankton by producing toxin and taking shelter. First, the existence and stability of the possible equilibria of system are explored. Next, the existence of Hopf bifurcation is investigated when the system has no time delay.

Bifurcation analysis in a singular Beddington-DeAngelis predator-prey model with two delays and nonlinear predator harvesting.

In this paper, a differential algebraic predator-prey model including two delays, Beddington-DeAngelis functional response and nonlinear predator harvesting is proposed. Without considering time delay, the existence of singularity induced bifurcation is analyzed by regarding economic interest as bifurcation parameter. In order to remove singularity induced bifurcation and stabilize the proposed system, state feedback controllers are designed in the case of zero and positive economic interest respectively.

Dynamics analysis of a predator-prey system with harvesting prey and disease in prey species.

In this paper, a predator-prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem.