Townley, Stuart (Univ. of Exeter), Ashwin, Peter (Univ. of Exeter), Wordsworth, John (Univ. of Exeter)

Dynamical Encoding, Learning and Control for Coupled Oscillator Systems

Scheduled for presentation during the Regular Session "Neural Networks II" (ThA12), Thursday, July 27, 2006, 11:15−11:40, Room 104b

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

The purpose of this paper is bring ideas from neuroscience, physics and dynamical systems together with those from control systems engineering and computer science. We focus on dynamical encoding of information. This is an important issue, not only in fundamental sciences, e.g., neuroscience, but also in numerous applications, e.g., future generation computing systems and control architectures.

The encoding of information has been the subject of several articles. In this paper we consider two approaches: encoding in Recurrent Neural Networks (RNNs) via parametrized limit cycles; encoding in coupled oscillators via symmetry induced heteroclinic cycles and clustered states. The former is more familiar in a context of control systems analysis and design. Indeed, the parametrized limit cycles lend themselves naturally to feedback control techniques. In particular, one can readily develop Lyapunov-based learning rules for convergent weight adaptation. The latter draws heavily on symmetry techniques from equivariant bifurcation theory and leads to very rich and complex dynamics. By borrowing and drawing on concepts and issues for the RNNs our aim is to formulate novel control system problems in a context of dynamically rich coupled oscillator systems.