Summary: Cluster synchronization, switching and spatiotemporal coding in a phase
, Peter Ashwin, John Wordsworth, and Stuart Townley
School of Engineering, Computing and Mathematics, University of Exeter, Exeter EX4 4QF, United Kingdom.
A network of five globally-coupled identical phase oscillators is considered. Cluster states consisting of two synchronized
pairs of oscillators and one singleton are investigated. Forcing the system with non-uniform constant inputs results in regular
switches between cluster states. The resultant cyclic sequences of switches (spatiotemporal codes) are studied for different
initial conditions and input configurations. Implications on information coding in neural systems are briefly discussed.
1 Cluster states in a phase oscillator model
We consider the phase oscillator model introduced in  for five identical oscillators with all-to-all coupling. The governing
ordinary differential equations are given by
n(t) = +
g n(t) - m(t) + p In , n = 1, . . . , 5 , (1)
where n(t) [0, 2) is the phase of the n-th oscillator, the dot represents differentiation with respect to the time t, is the
common natural frequency of oscillators and the coupling function is defined as g() = - sin(+)+r sin(2+). In this