Nowadays, research, modeling, simulation and realization of brain-like systems to reproduce brain behaviors have become urgent requirements. In this paper, neural bursting and synchronization are imitated by modeling two neural network models based on the Hopfield neural network (HNN). The first neural network model consists of four neurons, which correspond to realizing neural bursting firings. Theoretical analysis and numerical simulation show that the simple neural network can generate abundant bursting dynamics including multiple periodic bursting firings with different spikes per burst, multiple coexisting bursting firings, as well as multiple chaotic bursting firings with different amplitudes. The second neural network model simulates neural synchronization using a coupling neural network composed of two above small neural networks. The synchronization dynamics of the coupling neural network is theoretically proved based on the Lyapunov stability theory. Extensive simulation results show that the coupling neural network can produce different types of synchronous behaviors dependent on synaptic coupling strength, such as anti-phase bursting synchronization, anti-phase spiking synchronization, and complete bursting synchronization. Finally, two neural network circuits are designed and implemented to show the effectiveness and potential of the constructed neural networks.

中文翻译：

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神经网络和电路模拟的神经爆发和同步


如今，研究、建模、模拟和实现类脑系统以重现大脑行为已成为迫切需求。本文通过对基于 Hopfield 神经网络（HNN）的两个神经网络模型进行建模来模拟神经爆发和同步。第一个神经网络模型由四个神经元组成，对应于实现神经爆发。理论分析和数值模拟表明，简单的神经网络可以产生丰富的爆发动力学，包括每次爆发不同尖峰的多次周期性爆发、多个共存爆发以及不同幅度的多个混沌爆发。第二个神经网络模型使用由两个上述小型神经网络组成的耦合神经网络来模拟神经同步。基于Lyapunov稳定性理论，从理论上证明了耦合神经网络的同步动力学。大量的仿真结果表明，耦合神经网络可以根据突触耦合强度产生不同类型的同步行为，例如反相位突发同步、反相位尖峰同步和完全突发同步。最后，设计并实现了两个神经网络电路，以展示所构建的神经网络的有效性和潜力。