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...

We study in this paper the bifurcation and stability of the solutions of the Rayleigh-Bénard convection which has the infinite Prandtl number, using a notion of bifurcation called attractor bifurcation. We prove that the problem bifurcates from the trivial solution to an attractor AR when the Rayleigh number R crosses the first critical Rayleigh number Rc. As a special case, we also prove anoth...

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...

Percutaneous coronary intervention in the setting of coronary bifurcation lesions is associated with increased risk for complications. The goal of this manuscript is to review the currently available classifications for coronary artery bifurcation lesions with a guide to the use of specific coronary bifurcation techniques based on lesion characteristics. Iran J Med Sci 2008; 33(4): 187-194.

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

An explicit general formula is proposed for controlling Hopf bifurcation using state feedback. This method can be used to either delay (or even eliminate) an existing Hopf bifurcation or change a subcritical Hopf bifurcation to supercritical. The Lorenz system is used to illustrate the application of the formula.

In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out. Keywords—Nicholson,s blowflies model; Stability; Hopf bifurcation; Delay.

We study semilinear elliptic equations on general bounded domains with concave semipositone nonlinearities. We prove the existence of the maximal solutions, and describe the global bifurcation diagrams. When a parameter is small, we obtain the exact global bifurcation diagram. We also discuss the related symmetry breaking bifurcation when the domains have certain symmetries.