A model for the transmission of dengue fever with variable human population size is analyzed. We find three threshold parameters which govern the existence of the endemic proportion equilibrium, the increase of the human population size, and the behaviour of the total number of human infectives. We prove the global asymptotic stability of the equilibrium points using the theory of competitive s...

The dynamical behavior of an SIS epidemic model with birth pulses and pulse treatments at different moments is discussed by means of both theoretical and numerical ways. Birth pulse, vertical transmission, and pulse treatment are considered in building model. The existence and stability of the trivial solution, infection-free periodic solution, and epidemic periodic solutions are investigated. ...

We introduce a time-to-build technology in a Solow model with bounded technological progress. Our analysis shows that the system may be asymptotically stable, or it can produce stability switches and Hopf bifurcations when time delay varies. The direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. Nume...

In this paper, the van der Pol equation with a time delay is considered, where the time delay is regarded as a parameter. It is found that Hopf bifurcation occurs when this delay passes through a sequence of critical value. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions is given by using the normal form method and center manif...

This paper deals with a three-species ecological system with time delay and harvesting. Sufficient conditions guaranteeing the local stability and the occurrence of Hopf bifurcation for the system are obtained. Further, the properties of Hopf bifurcation are investigated using the center manifold theorem and normal form theory. Computer simulations are carried out to illustrate the theoretical ...

In this paper the dynamics of a discrete-time prey-predator system is investigated in the closed first quadrant . The existence and stability of fixed points are analyzed algebraically .The conditions of existence for flip bifurcation is derived by busing center manifold theorem and bifurcation theory. Numerical simulations not only illustrate our results but also exhibit complex dynamical beha...

The objective of this paper is to investigate the stability of limit cycles of a mathematical model with a distributed delay which describes the interaction between p53 and mdm2. Choosing the delay as a bifurca-tion parameter we study the direction and stability of the bifurcating periodic solutions using the normal form and the center manifold theorem. Some numerical examples are finally made ...

In this article, we consider the persistence of nontrivial traveling wave solutions of a bio-reactor system with strong generic delay kernels and nonlocal effect, which models the microbial growth in a flow reactor. By using the geometric singular perturbation theory and the center manifold theorem, we show that traveling wave solutions exist provided that the delays are sufficiently small with...

A bifurcation analysis is undertaken for a discrete-time Hopfield neural network with four delays. Conditions ensuring the asymptotic stability of the null solution are obtained with respect to two parameters of the system. Using techniques developed by Kuznetsov to a discrete-time system, we study the Neimark-Sacker bifurcation (also called Hopf bifurcation for maps) of the system. The directi...

A kind of fourth-order delay differential equation is considered. Firstly, the linear stability is investigated by analyzing the associated characteristic equation. It is found that there are stability switches for time delay and Hopf bifurcations when time delay cross through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form me...