Multimode dynamics in a network with resource mediated coupling

The purpose of this paper is to study the special forms of multimode dynamics that one can observe in systems with resource- mediated coupling, i. e., systems of self- sustained oscillators in which the coupling takes place via the distribution of primary resources that controls the oscillatory state of the individual unit.

With this coupling, a spatially inhomogenous state with mixed high and lowamplitude oscillations in the individual units can arise. To examine generic phenomena associated with this type of interaction we consider a chain of resistively coupled electronic oscillators connected to a common power supply.

The two- oscillator system displays antiphase synchronization, and it is interesting to note that two- mode oscillations continue to exist outside of the parameter range in which oscillations occur for the individual unit. At low coupling strengths, the multioscillator system shows high dimensional quasiperiodicity with little tendency for synchronization.

At higher coupling strengths, one typically observes spatial clustering involving a few oscillating units. We describe three different scenarios according to which the cluster can slide along the chain as the bias voltage changes.