Neurons are regarded as basic, structural and functional units of the central nervous system. They play an active role in the collection, storing and transferring of the information during signal processing in the brain. In this paper, we investigate the dynamics of a model of a 4D autonomous Hopfield neural network (HNN). Our analyses highlight complex phenomena such as chaotic oscillations, periodic windows, hysteretic dynamics, the coexistence of bifurcations and bursting oscillations. More importantly, it has been found several sets of synaptic weight for which the proposed HNN displays multiple coexisting stable states including three disconnected attractors. Besides the phenomenon of coexistence of attractors, the bursting phenomenon characterized by homoclinic/Hopf cycle–cycle bursting via homoclinic/fold hysteresis loop is observed. This contribution represents the first case where the later phenomenon (bursting oscillations) occurs in an autonomous HNN. Also, PSpice simulations are used to support the results of the previous analyses.

中文翻译：

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4D Hopfield 神经网络中多个稳定状态和突发振荡的共存

神经元被认为是中枢神经系统的基本、结构和功能单位。它们在大脑信号处理过程中对信息的收集、存储和传递起到积极的作用。在本文中，我们研究了 4D 自主 Hopfield 神经网络 (HNN) 模型的动力学。我们的分析突出了复杂的现象，例如混沌振荡、周期性窗口、滞后动力学、分岔和爆裂振荡的共存。更重要的是，已经发现了几组突触权重，所提出的 HNN 显示出多个共存的稳定状态，包括三个断开的吸引子。除了吸引子共存的现象外，还观察到了以同宿/Hopf循环-循环通过同宿/折叠滞后环爆发为特征的爆发现象。这种贡献代表了在自主 HNN 中发生后一种现象（爆发振荡）的第一种情况。此外，PSpice 模拟用于支持先前分析的结果。