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，将神经元系统与状态重置过程相结合。随着膜电位达到一定阈值，膜电位和恢复电流被重置。通过重置过程，神经元系统可以产生大量新的放电模式。通过与状态重置过程相结合，神经元系统可以产生不规则的极限环（具有脉冲断点的极限环），从而导致重复的尖峰或突发，其发射峰值不能超过预设阈值。尽管一些研究已经讨论了神经元中的状态重置过程，但到目前为止还没有在神经网络中得到解决。在本文中，我们考虑了具有状态重置过程的 Hindmarsh-Rose 神经网络中的嵌合状态和集群解决方案。网络结构基于规则的环形结构，并且假设神经元之间的连接是双向的。嵌合体和集群状态是与同步相关的两种现象。对于神经网络，嵌合状态是一种自组织现象，其中一些神经元节点是同步的，而另一些是异步的。集群同步根据系统的同步特性将系统分为几个子组，每个子组中的神经元节点是同步的。通过改进以前的嵌合体测量，我们检测尖峰激发时间而不是状态变量，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。此外，我们进一步对比了系统在局部和全局耦合下的集群解决方案，分别。从属状态重置过程丰富了所提出的 Hindmarsh-Rose 神经网络的触发模式。