Zhouchao Wei∗ School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P. R. China Division of Dynamics, Technical University of Lodz, Lodz, Stefanowskiego 1/15, 90-924, Poland College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, P. R. China Mathematical Institute, University of Oxford, Oxford, OX2 6GG, England [email protected]...

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 ...

In this paper, the bursting oscillation phenomenon in coupled systems with two time scales is introduced. Firstly, several types of bifurcation are briefly introduced: fold bifurcation, Hopf limit cycle homoclinic etc. The oscillations system excitation terms and delay considered. Secondly, some simple introduced, such as fold/fold bursting, fold/supHopf subHopf/subHopf fold/LPC Hopf/LPC fold/h...

In this paper, a special SEIR epidemic model with nonlinear incidence rates is considered. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when these delays pass through a sequence of critical value. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf ...

Electroconvection in nematic liquid crystals exhibits a Hopf bifurcation to traveling rolls for a wide parameter range. The model normally used to describe electroconvection fails to predict this. A recent theoretical extension, the weak-electrolyte model, incorporates the dissociation-recombination reaction of the ionic dopant in the sample and does predict a Hopf bifurcation for a range of pa...

This paper deals with the dynamics of food web consisting of two logistic preys and a variable harvesting predator of Modified LeslieGower type. The existence of Hopf bifurcation analysis with varying key parameter is investigated.

The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The results are used to compare delayed versus undelayed feedback, as well as discrete versus distributed delays. Conditions are obtained for which delayed feedback...

In this paper, a coupled FHN model with two different delays is investigated. The local stability and the existence of Hopf bifurcation for the system are analyzed. The effect of two different delays on dynamical behavior is discussed. Simulation results are presented to support theoretical analysis. Finally, main conclusions are included.

This chapter deals with bifurcation dynamics in control systems, which are described by ordinary differential equations, partial differential equations and delayed differential equations. In particular, bifurcations related to double Hopf, combination of double zero and Hopf, and chaos are studied in detail. Center manifold theory and normal form theory are applied to simplify the analysis. Exp...