Yang Yi, Xiang Changcheng, Dai Xiangguang, Zhang Xianxiu, Qi Liyuan, Zhu Bingli, Dong Tao
College of Computer Science and Engineering, Chongqing Three Gorges University, Chongqing, 404100 China.
Key Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher Education, Chongqing Three Gorges University, Chongqing, 404100 China.
Cogn Neurodyn. 2022 Feb;16(1):215-228. doi: 10.1007/s11571-021-09691-0. Epub 2021 Jun 30.
The neuronal state resetting model is a hybrid system, which combines neuronal system with state resetting process. As the membrane potential reaches a certain threshold, the membrane potential and recovery current are reset. Through the resetting process, the neuronal system can produce abundant new firing patterns. By integrating with the state resetting process, the neuronal system can generate irregular limit cycles (limit cycles with impulsive breakpoints), resulting in repetitive spiking or bursting with firing peaks which can not exceed a presetting threshold. Although some studies have discussed the state resetting process in neurons, it has not been addressed in neural networks so far. In this paper, we consider chimera states and cluster solutions in Hindmarsh-Rose neural networks with state resetting process. The network structures are based on regular ring structures and the connections among neurons are assumed to be bidirectional. Chimera and cluster states are two types of phenomena related to synchronization. For neural networks, the chimera state is a self-organization phenomenon in which some neuronal nodes are synchronous while the others are asynchronous. Cluster synchronization divides the system into several subgroups based on their synchronization characteristics, with neuronal nodes in each subgroup being synchronous. By improving previous chimera measures, we detect the spike inspire time instead of the state variable and calculate the time between two adjacent spikes. We then discuss the incoherence, chimera state, and coherence of the constructed neural networks using phase diagrams, time series diagrams, and probability density histograms. Besides, we further contrast the cluster solutions of the system under local and global coupling, respectively. The subordinate state resetting process enriches the firing mode of the proposed Hindmarsh-Rose neural networks.
神经元状态重置模型是一个混合系统，它将神经元系统与状态重置过程相结合。当膜电位达到某个阈值时，膜电位和恢复电流会被重置。通过重置过程，神经元系统可以产生丰富的新放电模式。通过与状态重置过程相结合，神经元系统可以生成不规则的极限环（具有脉冲断点的极限环），从而导致重复的尖峰放电或爆发，其放电峰值不会超过预设阈值。尽管一些研究讨论了神经元中的状态重置过程，但到目前为止在神经网络中尚未涉及。在本文中，我们考虑具有状态重置过程的 Hindmarsh-Rose 神经网络中的嵌合态和簇解。网络结构基于规则的环结构，并且假设神经元之间的连接是双向的。嵌合态和簇态是与同步相关的两种现象。对于神经网络而言，嵌合态是一种自组织现象，其中一些神经元节点是同步的，而其他节点是异步的。簇同步根据其同步特性将系统划分为几个子组，每个子组中的神经元节点是同步的。通过改进先前的嵌合度量，我们检测的是尖峰激发时间而非状态变量，并计算两个相邻尖峰之间的时间。然后，我们使用相图、时间序列图和概率密度直方图来讨论所构建神经网络的非相干性、嵌合态和相干性。此外，我们还分别进一步对比了系统在局部耦合和全局耦合下的簇解。从属的状态重置过程丰富了所提出的 Hindmarsh-Rose 神经网络的放电模式。
