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...

UMIST The use of boundary locus plots in the identiication of bifurcation points in numerical approximation of delay diierential equations Abstract We are interested in nonlinear delay diierential equations which have a Hopf bifurcation. We assume zero is a steady state for the problem, and so a Hopf bifurcation point lies on the boundary of the region of asymptotic stability for the zero solut...

This paper is concerned with a delayed SIRS epidemic model with a nonlinear incidence rate. The main results are given in terms of local stability and Hopf bifurcation. Sufficient conditions for the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained by regarding the time delay as the bifurcation parameter. Further, the properties of Hopf bifurcation such ...

A subcritical Hopf bifurcation in a dynamical system modeled by a scalar nonlinear delay differential equation is studied theoretically and experimentally. The subcritical Hopf bifurcation leads to a significant domain of bistability where stable steady and time-periodic states coexist.

The aim of this paper is to study Hopf bifurcation with Dn-symmetry assuming Birkhoff normal form. We consider the standard action of Dn on C. This representation is absolutely irreducible and so the corresponding Hopf bifurcation occurs on C ⊕ C. Golubitsky and Stewart (Hopf bifurcation with dihedral group symmetry: Coupled nonlinear oscillators. In: Multiparameter Bifurcation Series (M. Golub...

Using a drift flux representation for the two-phase flow, a new reduced order model has been developed to simulate density-wave oscillations (DWOs) in a heated channel. This model is then used to perform stability and semi-analytical bifurcation analysis, using the bifurcation code BIFDD, in which the stability boundary (SB) and the nature of Hopf bifurcation are determined in a suitable two-di...

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