Abstract. Systems of globally coupled phase oscillators can have robust attractors that are heteroclinic networks. We investigate such a heteroclinic network between partially synchronized states where the phases cluster into three groups. For the coupling considered there exist 30 different three-cluster states in the case of five oscillators. We study the structure of the heteroclinic network and demonstrate that it is possible to navigate around the network by applying small impulsive inputs to the oscillator phases. This paper shows that such navigation may be done reliably even in the presence of noise and frequency detuning, as long as the input amplitude dominates the noise strength and the detuning magnitude, and the time between the applied pulses is in a suitable range. Furthermore, we show that, by exploiting the heteroclinic dynamics, frequency detuning can be encoded as a spatiotemporal code. By changing a coupling parameter we can stabilize the three-cluster states and replace the heteroclinic network by a network of excitable three-cluster states. The resulting "excitable network" has the same structure as the heteroclinic network and navigation around the excitable network is also possible by applying large impulsive inputs. We also discuss features that have implications for related models of neural activity.

We investigate the spatiotemporal coding of low amplitude inputs to a simple system of globally coupled phase oscillators with coupling function g͑͒ = −sin͑ + ␣͒ + r sin͑2 + ␤͒ that has robust heteroclinic cycles ͑slow switching between cluster states͒. The inputs correspond to detuning of the oscillators. It was recently noted that globally coupled phase oscillators can encode their frequencies in the form of spatiotemporal codes of a sequence of cluster states ͓P. Ashwin, G. Orosz, J. Wordsworth, and S. Townley, SIAM J. Appl. Dyn. Syst. 6, 728 ͑2007͔͒. Concentrating on the case of N = 5 oscillators we show in detail how the spatiotemporal coding can be used to resolve all of the information that relates the individual inputs to each other, providing that a long enough time series is considered. We investigate robustness to the addition of noise and find a remarkable stability, especially of the temporal coding, to the addition of noise even for noise of a comparable magnitude to the inputs.

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.