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Summary: 611
Progress of Theoretical Physics, Vol. 122, No. 3, September 2009
Designing the Dynamics of Globally Coupled Oscillators
G´abor Orosz,1,2 Jeff Moehlis1 and Peter Ashwin2
1Department of Mechanical Engineering, University of California,
Santa Barbara, California 93106, USA
2School of Engineering, Computing and Mathematics, University of Exeter,
Exeter EX4 4QF, UK
(Received May 15, 2009)
A method for designing cluster states with prescribed stability is presented for coupled
phase oscillator systems with all-to-all coupling. We determine criteria for the coupling
function that ensure the existence and stability of a large variety of clustered configurations.
We show that such criteria can be satisfied by choosing Fourier coefficients of the coupling
function. We demonstrate that using simple trigonometric and localized coupling functions
one can realize arbitrary patterns of stable clusters and that the designed systems are ca-
pable of performing finite state computation. The design principles may be relevant when
engineering complex dynamical behavior of coupled systems, e.g. the emergent dynamics of
artificial neural networks, coupled chemical oscillators and robotic swarms.
Subject Index: 034, 044, 054, 055
§1. Introduction
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