The dynamics of a delayed mathematical model for Hes1 oscillatory expression are investigated. The linear stability of positive equilibrium and existence of local Hopf bifurcation are studied. Moreover, the global existence of large periodic solutions has been established due to the global bifurcation theorem. Keywords—Hes1, Hopf bifurcation, time delay, transcriptional repression loop

this paper is devoted to study of a partial differential equation governing panel motion in supersonic flow. this pde can be transformed to an ode by means of a galerkin method. here by using a criterion which is closely related to the routh-hurwitz criterion, we investigate the mentioned transformed ode from hopf bifurcation point of view. in fact we obtain a region for existence of simple hop...

This paper focuses on Hopf bifurcation control in a dual model of Internet congestion control algorithms which is modeled as a delay differential equation (DDE). By choosing communication delay as a bifurcation parameter, it has been demonstrated that the system loses stability and a Hopf bifurcation occurs when communication delay passes through a critical value. Therefore, a time-delayed feed...

We establish an analytic local Hopf bifurcation theorem and a topological global Hopf bifurcation theorem to detect the existence and to describe the spatial-temporal pattern, the asymptotic form and the global continuation of bifurcations of periodic wave solutions for functional differential equations in the presence of symmetry. We apply these general results to obtain the coexistence of mul...

We consider a simplified bidirectional associated memory (BAM) neural network model with four neurons andmultiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson’s criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown th...

Jerk systems with delayed feedback are considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associated characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, the stability and direction of the Hopf bifurcation are determined by applying the normal form method and center manifold theorem. Fina...

A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory ...

For a two-neuron network with self-connection and time delays, we carry out stability and bifurcation analysis. We establish that a Hopf bifurcation occurs when the total delay passes a sequence of critical values. The stability and direction of the local Hopf bifurcation are determined using the normal form method and center manifold theorem. To show that periodic solutions exist away from the...

Taking the delay due to the latent period of computer viruses and the delay due to the period that the anti-virus software uses to clean the computer viruses as the bifurcation parameters, local Hopf bifurcation of an epidemic model over the Internet is studied. We discuss the existence of the Hopf bifurcation under four conditions: (1) τ1 > 0, τ2 = 0, (2) τ1 = 0, τ2 > 0, (3) τ1 = τ2 = τ > 0, a...

In this paper we prove that periodic boundary-value problems (BVPs) for delay differential equations are locally equivalent to finite-dimensional algebraic systems of equations. We rely only on regularity assumptions that follow those of the review by Hartung et al. (2006). Thus, the equivalence result can be applied to differential equations with state-dependent delays (SD-DDEs), transferring ...