We consider as a mathematical model of human cortical electrical activity a system of fourteen ordinary differential equations. With appropriate parameters, the model produces activity characteristic of a seizure. To prevent such seizures, we incorporate feedback controllers into the model dynamics. We show that three controllers--a linear feedback controller, a differential controller, and a f...

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a g...

The relevance of bifurcation analysis in Takagi–Sugeno (T–S) fuzzy systems is emphasized mainly through examples. It is demonstrated that even the most simple cases can show a great variety of behaviors. To understand the richness of asymptotic dynamics, one can find in T–S systems, a methodology is proposed by invoking bifurcation theory. Several local and global bifurcations (some of them, de...

In this paper, we build a model of energy-savings and emission-reductions with two delays. In this model, it is assumed that the interaction between energy-savings and emission-reduction and that between carbon emissions and economic growth are delayed. We examine the local stability and the existence of a Hopf bifurcation at the equilibrium point of the system. By employing System Complexity T...

This paper discusses feed-forward chains near points of synchrony-breaking Hopf bifurcation. We show that at synchrony-breaking bifurcations the center manifold inherits a feed-forward structure and use this structure to provide a simplified proof of the theorem of Elmhirst and Golubitsky that there is a branch of periodic solutions in such bifurcations whose amplitudes grow at the rate of λ 1 ...

Based on the earlier research results, and combined with the actual competition in Chinese insurance market, the triopoly dynamic game model is built under the hypothesis that the oligarchs make adaptive decision, delayed bounded rational decision and bounded rational decision respectively. The existence of only Nash equilibrium in the system is analyzed theoretically, and its stability and the...

{In many power systems, the operating margin may be investigated and improved by considering the bifurcations in their models. Control of (unstable) bifur-cations, i.e. delay or elimination of them, may be possible through feedback linearizing control. Two major issues in implementing this approach are the relative degree of the system and the eeects of model uncertainties. In this work, contro...

We report on the feedback control of a periodically driven FitzHugh-Nagumo system displaying various dynamical regimes, regular and chaotic, including chaotic spiking. The feedback term is composed of a high-pass or an all-pass filter. We provide a characterization of the efficiency of the filters in controlling the dynamical state of the system, both experimentally (electronic circuit) and num...

{ Bifurcation analysis provides a methodology for the study of the changes of stability behavior of nonlinear and parameter dependent systems. The inception of bifurcations is associated with systems exhibiting critical modes. Consequently, stabilization of critical systems can be considered as control of the underlying bifurcations. Based on bifurcation equations and the center manifold theore...