Essential instabilities of fronts: bifurcation, and bifurcation failure

Bifurcation to fronts due to delay.

The stability of a steady-state front (kink) subject to a time-delayed feedback control (TDFC) is examined in detail. TDFC is based on the use of the difference between system variables at the current moment of time and their values at some time in the past. We first show that there exists a bifurcation to a moving front. We then investigate the limit of large delays but weak feedback and obtai...

Instabilities, Bifurcation and Saddle-points in Some Fbp's in Combustion

Turing instabilities and patterns near a Hopf bifurcation

Rui Dilão Grupo de Dinâmica Não-Linear, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal. and Institut des Hautes Études Scientifiques, 35, route de Chartres, 91440, Bures-sur-Yvette, France. [email protected] Phone: +(351) 218417617; Fax: +(351) 218419123 Abstract We derive a necessary and sufficient condition for Turing instabilities to occur in twocomponent systems of ...

Hopf bifurcation from fronts in the Cahn-Hilliard equation

We study Hopf bifurcation from traveling-front solutions in the Cahn-Hilliard equation. The primary front is induced by a moving source term. Models of this form have been used to study a variety of physical phenomena, including pattern formation in chemical deposition and precipitation processes. Technically, we study bifurcation in the presence of essential spectrum. We contribute a simple an...

Bifurcation analysis and dynamics of a Lorenz –type dynamical system 

./files/site1/files/0Abstract1.pdfIn this paper we consider a continues Lorenz – type dynamical system. Dynamical behaviors of this system such as computing equilibrium points, different bifurcation curves and computation of normal form coefficient of each bifurcation point analytically and numerically. In particular we derived sufficient conditions for existence of Hopf and Pitchfork bifurcati...