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Chimera states and cluster solutions in Hindmarsh-Rose neural networks with state resetting process

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Abstract

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.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 11961024, in part by Youth Project of Scientific and Technological Research Program of Chongqing Education Commission (KJQN201901203, KJQN201901218), in part by Chongqing higher education reform research project (203443,203447), in part by Foundation of Chongqing Municipal Key Laboratory of Institutions of Higher Education ([2017]3), in part by Foundation of Chongqing Development and Reform Commission (2017[1007]), in part by Foundation of Chongqing Three Gorges University, in part by the Chongqing Technological Innovation and Application Project under Grant cstc2018jszx-cyzdX0171, in part by Chongqing Basic and Frontier Research Project under Grant cstc2019jcyj-msxm2105, in part by the Science and Technology Research Program of Chongqing Municipal Education Commission under Grant KJQN201900816, in part by Chongqing Social Science Planning Project under Grant 2019BS053.

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Authors and Affiliations

  1. College of Computer Science and Engineering, Chongqing Three Gorges University, Chongqing, 404100, China

    Yi Yang, Xiangguang Dai, Xianxiu Zhang, Liyuan Qi & Bingli Zhu

  2. Key Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher Education, Chongqing Three Gorges University, Chongqing, 404100, China

    Yi Yang, Xiangguang Dai, Xianxiu Zhang, Liyuan Qi & Bingli Zhu

  3. School of Mathematics and Statistics, Hubei Minzu University, Enshi, 445000, China

    Changcheng Xiang

  4. College of Electronics and Information Engineering, Southwest University, Chongqing, 400715, China

    Tao Dong

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  1. Yi Yang
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Yang, Y., Xiang, C., Dai, X. et al. Chimera states and cluster solutions in Hindmarsh-Rose neural networks with state resetting process. Cogn Neurodyn 16, 215–228 (2022). https://doi.org/10.1007/s11571-021-09691-0

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