In this paper, a delayed SIS (Susceptible Infectious Susceptible) model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center man-ifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to… (More)
In this paper, by using the Mawhin's continuation theorem, we prove the existence of periodic solutions for a stage-structure ecological model on time scales. This unifies the results for differential and difference equations.
—The main purpose of this paper is to investigate a discrete time three–species food chain system with ratio dependence. By employing coincidence degree theory and analysis techniques, sufficient conditions for existence of periodic solutions are established .
In this paper, a modified delayed mathematical model for the dynamics of HIV with cure rate is considered. By regarding the time delay as bifurcation parameter, stability and existence of local Hopf bifurcation are studied by analyzing the transcendental characteristic equation. Then the global existence of bifurcating periodic solutions is established with… (More)
In this paper, a delay model of plankton allelopathy is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. The presented criteria improve and extend previous results in the literature.
Viruses have important influences on human health: they not only cause some common diseases, but also cause serious illnesses. Moreover, the conventional medicines usually fail to prevent or treat them, and viral infections are hard to treat because viruses live inside the body's cells. However, some mathematical models can help to understand the viral… (More)
The diffusive logistic growth model with time delay and feedback control is considered. First, the well-posedness and permanence of solutions are discussed by using some comparison techniques. Then, the sufficient conditions for stability of nonnegative constant steady states are established, and the occurrence of Hopf bifurcation at positive steady state… (More)
—This paper is concerned with a nonautonomous three species food chain model with Crowley–Martin type functional response and time delay. Using the Mawhin's continuation theorem in theory of degree, sufficient conditions for existence of periodic solutions are obtained.
In this paper, a discrete disease spreading model in complex networks with time delay is investigated. The stability of positive equilibrium and existence of Hopf bifurcation are explored by analyzing the associated characteristic equation. Furthermore, a numerical example is given.
In this paper, our attention is focused on the global existence of bifurcating periodic solutions. We show that periodic solutions exist after the second critical value of time delay. Furthermore, a numerical example is given.