Travelling waves in an ensemble of excitable oscillators: the interplay of memristive coupling and noise

Ivan A. Korneev, Ibadulla R. Ramazanov, Andrei V. Slepnev, Tatiana E. Vadivasova, Vladimir V. Semenov
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Abstract

Using methods of numerical simulation, we demonstrate the constructive role of memristive coupling in the context of the travelling waves 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 on an example of the deterministic model where the memristive properties of the coupling elements provide for achieving travelling 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 travelling waves as compared to classical diffusive interaction. In addition, we point out the second constructive factor, the L{\'e}vy noise whose properties provide for inducing travelling waves.
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可激发振荡器集合中的游波:记忆耦合与噪声的相互作用
通过数值模拟的方法,我们证明了记忆耦合在菲茨休-纳古莫神经元模型描述的可兴奋振荡器集合中的行波形成和稳健性方面的建设性作用。首先,在确定性模型的一个例子中展示了记忆耦合作用的揭示方面,与非适应性扩散耦合相比,耦合元件的记忆特性可以在较低的耦合强度下实现行波。在存在噪声的情况下,记忆耦合的积极作用表现为噪声强度临界值的显著增加,与经典的扩散相互作用相比,噪声导致的行波破坏与之相对应。此外,我们还指出了第二个构造因子--L{'e}vy噪声,它的特性为诱导行波提供了条件。
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