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.

研究了通过忆阻元件耦合的FitzHugh-Nagumo（FHN）振荡器的环。忆阻元件初始状态对行波特性的影响是针对各个振荡器的自激振动和激励动力学而建立的。结果表明，在可激发状态下，初始状态的影响尤为明显。在这种情况下，忆阻元件状态的初始分布会影响波的空间分布以及脉冲激励的频率。对具有理想忆阻器耦合的集成的研究得到了模型探索的补充，该模型隐含了通过忆阻器进行交互的特征，该忆阻器的特征是随着时间的推移“忘记”了初始状态。