Designing the dynamics of globally coupled oscillators
Orosz, Gábor; Moehlis, Jeff; Ashwin, Peter
Date: 1 September 2009
Article
Journal
Progress of Theoretical Physics
Publisher
Oxford University Press
Publisher DOI
Abstract
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 ...
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 capable 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.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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