Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network

We consider a two-layer multiplex network of diffusively coupled FitzHugh-Nagumo (FHN) neurons in the excitable regime. We show that the phenomenon of coherence resonance (CR) in one layer can not only be controlled by the network topology, the intra-and interlayer time-delayed couplings, but also by another phenomenon, namely, self-induced stochastic resonance (SISR) in the other layer. Numerical computations show that when the layers are isolated, each of these noise-induced phenomena is weakened (strengthened) by a sparser (denser) ring network topology, stronger (weaker) intralayer coupling forces, and longer (shorter) intralayer time delays. However, CR shows a much higher sensitivity than SISR to changes in these control parameters. It is also shown, in contrast to SISR in a single isolated FHN neuron, that the maximum noise amplitude at which SISR occurs in the network of coupled FHN neurons is controllable, especially in the regime of strong coupling forces and long time delays. In order to use SISR in the first layer of the multiplex network to control CR in the second layer, we first choose the control parameters of the second layer in isolation such that in one case CR is poor and in another case, nonexistent. It is then shown that a pronounced SISR can not only significantly improve a poor CR, but can also induce a pronounced CR, which was nonexistent in the isolated second layer. In contrast to strong intralayer coupling forces, strong interlayer coupling forces are found to enhance CR, while long interlayer time delays, just as long intralayer time delays, deteriorate CR. Most importantly, we find that in a strong interlayer coupling regime, SISR in the first layer performs better than CR in enhancing CR in the second layer. But in a weak interlayer coupling regime, CR in the first layer performs better than SISR in enhancing CR in the second layer. Our results could find novel applications in noisy neural network dynamics and engineering.