The impact of memristive coupling initial states on travelling waves in an ensemble of the FitzHugh–Nagumo oscillators

A ring of the FitzHugh–Nagumo (FHN) oscillators coupled via memristive elements is studied. The impact of the memristive element initial states on the travelling wave characteristics is established for the self-oscillatory and excitable dynamics of the individual oscillators. It is shown that the initial state effect is especially evident in the excitable regime. In such a case the initial distribution of the memristive element states affects on the wave spatial profile as well as on the frequency of the pulse excitation. The study of the ensemble with ideal memristor coupling is complemented by the exploration of the model implying the interaction through the memristor characterized by 'forgetting' the initial states over time. It is demonstrated through this approach that the dependence of the oscillation characteristics on the memristor initial states persists in the presence of the weak memristor imperfectness.