Transmitting a signal by amplitude modulation in a chaotic network

We discuss the ability of a model of network with nonlinear units and chaotic dynamics to transmit signals, on the basis of a linear response theory developed by Ruelle [D. Ruelle, J. Stat. Phys. 95, 393 (1999)] for dissipative systems. We discuss in particular how the dynamics may interfere with the graph topology to produce an effective transmission network, whose topology depends on the signal, and cannot be directly read on the "wired" network. Then, we show examples where, with a suitable choice of the carrier frequency (resonance), one can transmit a signal from a node to another one by amplitude modulation, in spite of chaos. Also, we give an example where a signal, transmitted to any node via different paths, can only be recovered by a couple of specific nodes. This opens up the possibility for encoding data in a way such that the recovery of the signal requires the knowledge of the carrier frequency and can be performed only at some specific node.

Stable resonances and signal propagation in a chaotic network of coupled units

We apply the linear response theory developed by Ruelle [J. Stat. Phys. 95, 393 (1999)] to analyze how a periodic signal of weak amplitude, superimposed upon a chaotic background, is transmitted in a network of nonlinearly interacting units. We numerically compute the complex susceptibility and show the existence of specific poles (stable resonances) corresponding to the response to perturbations transverse to the attractor. Contrary to the poles of correlation functions they depend on the pair emitting-receiving units. This dynamic differentiation, induced by nonlinearities, exhibits the different ability that units have to transmit a signal in this network.