Inertial manifolds and master-slave synchronization


主讲人:Bj?rn Schmalfuss,Friedrich Schiller University Je




内容介绍:We consider dynamical systems and random dynamical systems. We present objects ?describing the long time behavior of these systems. Particular objects are ?attractors and inertial manifolds. Both objects allow to introduce the concept ?of small finite dimensionality of high/infinite dynamical systems. We will ?consider inertial manifolds in more details. Two techniques allowing to state ?these manifolds are the Lyapunov Perron transform and the graph transform. We ?will consider the dynamics on these manifolds by the inertial form. Attractors ?and inertial manifolds can be used to describe synchronization of two or more ?parallel systems. We will describe the main issues of this topic. All these ?things will be applied to random and non-random reaction diffusion equations.