Traveling waves in an ensemble of excitable oscillators: The interplay of memristive coupling and noise

Using methods of numerical simulation, we demonstrate the constructive role of memristive coupling in the context of the traveling wave formation and robustness in an ensemble of excitable oscillators described by the FitzHugh-Nagumo neuron model. First, the revealed aspects of the memristive coupling action are shown in an example of the deterministic model where the memristive properties of the coupling elements provide for achieving traveling waves at lower coupling strength as compared to non-adaptive diffusive coupling. In the presence of noise, the positive role of memristive coupling is manifested as significant, increasing a noise intensity critical value corresponding to the noise-induced destruction of traveling waves as compared to classical diffusive interaction. In addition, we point out the second constructive factor, the Lévy noise, whose properties provide for inducing traveling waves.