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.
