Image Representation through Synchronisation and Generalised Turing Patterns in Networks of Coupled Dynamical SysteMS

Abstract

The phenomenon of synchronisation in coupled dynamical systems, and in particular, the conditions under which such coupled systems achieve synchrony is a topic of current interest and potential applications. The main objective of the present project has been to explore a technique by which an image can be represented with a network of coupled dynamical systems in terms of the coupling matrix of the network. The central concept is the use of the Lyapunov exponent in determining the bounds within which a network of dynamical systems will show globally synchronous behaviour. The concept of a Lyapunov spectrum has been used to determine the conditions for which perturbations around the synchronous trajectory damp over time, implying a stable globally synchronous state. For coupling schemes outside these bounds one observes specific patterns, termed Generalised Turing Patterns; this work presents application of this method to represent a given image with a network of coupled dynamical systems. The effectiveness of the method is shown through a few test cases. The method can be an effective tool in image reconstruction/retrieval; certain directions of improvement are outlined.