—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.
—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 delayed model of gene expression with positive feedback loop is investigated. The model takes the form of delay differential equations. By choosing the time delay as bifurcation parameter, small amplitude periodic solutions are obtained due to Hopf bifurcation. Furthermore, global existence of bifurcating periodic solutions is established… (More)
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.
—In this paper, a tri–neuron network model with time delay is investigated. By using the Bendixson's criterion for high– dimensional ordinary differential equations and global Hopf bifurca-tion theory for functional differential equations, sufficient conditions for existence of periodic solutions when the time delay is sufficiently large are established.