The coupling between neuronal oscillators plays an intriguing role in understanding the dynamics of the biological neurons present in realistic situations. Importantly, when the coupling between these neurons assumes an asymmetric nature, it can lead to profound changes in their overall behavior. In order to explore the impact of asymmetrical coupling on neuron models subjected to magnetic flux induction, we employ a coupled Tabu learning neuron model. Specifically, we illustrate the interplay between flux coupling and asymmetric electrical synapses concerning the control parameters of the proposed system using phase portraits, time series, bifurcation analysis, and Lyapunov spectrum. In particular, we show the dynamics by taking into account asymmetric interactions between neurons, from a simple network of two coupled systems to a network of nodes. Primarily, we demonstrate that two coupled systems exhibit synchronization for a fixed magnitude of control parameter with increasing coupling strength. Furthermore, we discuss the collective dynamics for the distinct network connectivity including regular, small-world and random. For all network connections, an increase in coupling strength facilitates a transition from desynchronization to synchronization via chimera state. We believe that attaining synchronization in Tabu learning neuron can act as a pivotal factor for neuron activity, contributing to the realization of such behavior in the context of numerous cognitive processes.

中文翻译：

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非对称耦合忆阻 Tabu 学习神经元网络中的同步和嵌合体


神经元振荡器之间的耦合在理解现实情况下存在的生物神经元的动力学方面起着有趣的作用。重要的是，当这些神经元之间的耦合呈现出不对称的性质时，它会导致它们的整体行为发生深刻的变化。为了探讨不对称耦合对受磁通量感应的神经元模型的影响，我们采用了耦合的 Tabu 学习神经元模型。具体来说，我们使用相位图、时间序列、分叉分析和 Lyapunov 谱来说明磁通耦合和非对称电突触之间关于所提出系统的控制参数之间的相互作用。特别是，我们通过考虑神经元之间的不对称相互作用来展示动力学，从两个耦合系统的简单网络到节点网络。首先，我们证明了两个耦合系统在固定幅度的控制参数下表现出同步性，耦合强度不断增加。此外，我们还讨论了不同网络连接的集体动力学，包括常规、小世界和随机。对于所有网络连接，耦合强度的增加有助于从不同步过渡到通过 chimera 状态进行同步。我们相信，在 Tabu 学习神经元中实现同步可以作为神经元活动的关键因素，有助于在众多认知过程的背景下实现这种行为。