Title : The generalised synchronization of dynamical systems: Geometry and Constraints.
Speaker : Prof. Ramakrishna Ramaswamy, IIT Delhi
Date : 13/10/2022, 05:30 PM , Online.
The generalised synchronization of coupled dynamical systems is a state of strong correlation, when the dynamics of one system is uniquely dependent on that of the other. We discuss how this can be seen in geometric terms, as a confinement of the dynamics to lower dimensional submanifolds in the phase space. In this framework, synchronization is seen as a process of imposing algebraic constraints which may also be time-dependent. We propose a procedure for constructing (non-unique) coupling functions that can guide the flow to the desired submanifold which can also be made stable and attracting. A geometric analysis of the stability of this manifold is provided, and the procedure is demonstrated through representative examples.