This is a brief survey of some recent developments in the study of infinite dimensional Hopf algebras which are either noetherian or have finite Gelfand-Kirillov dimension. A number of open questions are listed.

This brief attempts to study the low-frequency bifurcation phenomena of a system of parallel-connected dc/dc boost converters. Analysis of the averaged state equations shows that the system loses stability via a Hopf bifurcation. The loci of eigenvalues and the local trajectories are studied. Computer simulations and experiments are performed to capture the effects of variation of some chosen p...

We analyze a differential-algebraic biological economic system with time delay. The model has two different Holling functional responses. By considering time delay as bifurcation parameter, we find that there exists stability switches when delay varies, and the Hopf bifurcation occurs when delay passes through a sequence of critical values. Furthermore, we also consider the stability and direct...

For differential-algebraic power systems, saddle-noddle bifurcation and Hopf bifurcation are both of universally existent phenomena in power systems. Usually Newton iteration method could be applied to the Moore-Spence system to compute saddle-noddle and Hopf bifurcation points directly. But the Moore-Spence system has very high dimension and causes much complexity in Jacobian matrix factorizat...

In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given...

The dynamics of a system of two semiconductor lasers, which are delay coupled via a passive relay within the synchronization manifold, are investigated. Depending on the coupling parameters, the system exhibits synchronized Hopf bifurcation and the stability switches as the delay varies. Employing the center manifold theorem and normal form method, an algorithm is derived for determining the Ho...

Abstract. Based on facts of time delay will influence dynamical behavior and control theory is more appropriate to reflect the natural rule, constructed a predator-prey control model with two delays,choose the two delays as the bifurcation parameter,according to the Routh-Hurwize discriminant method,we studied the local stability and Hopf branch of the control system.The sufficient conditions f...

A recent paper Ncube (2013) [11] considered the disease-free equilibrium in a mathematical model for intra-host dynamics of Plasmodium falciparum malaria with discrete immune time delay. The author showed that depending on system parameters, the disease-free steady state can be absolutely stable (i.e. asymptotically stable for arbitrary positive values of the time delay), or it can be asymptoti...

In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verif...

We apply our recently developed global Hopf bifurcation theory to examine global continuation with respect to the parameter for periodic solutions of functional differential equationswith state-dependent delay.We give sufficient geometric conditions to ensure the uniform boundedness of periodic solutions, obtain an upper bound of the period of nonconstant periodic solutions in a connected compo...