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.