Discrete computation using a perturbed heteroclinic network

Copyright © 2005 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physics Letters A, Vol 347, Issues 4-6, 2005, DOI: 10.1016/j.physleta.2005.08.013Transient synchronization into clusters appears in many biological and physical systems and seems to be important for computation within neural systems. In this paper we show how one can robustly and effectively perform practical computations using small perturbations to a very simple globally coupled network of oscillators. Computations are performed by exploiting the spatio-temporal dynamics of a robust attracting heteroclinic network (also referred to as `winnerless competition' dynamics) to describe the states and transitions between them. We use different cluster synchronization states to encode states and use this to design a simple multi-base counter. The simulations indicate that this gives a robust computational system exploiting the natural dynamics of the system