Designing the Dynamics of Globally Coupled Oscillators

'Progress of Theoretical Physics' is the predecessor journal to 'Progress of Theoretical and Experimental Physics (PTEP)'. PTP terminated in December 2012 and merged into PTEP in January 2013.Copyright © 2009 The Physical Society of JapanA 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