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Response solutions for a kind of quasi-periodic forced neuron system

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  • Ren, Xiufang
  • Lu, Yao
  • Luo, Jie
  • Zeng, Xudong

Abstract

Based on the transcranial magnetic stimulation (TMS) therapy for major depression disorder and anxiety disorder, an abstract form of neuron differential equation with quasi-periodic coefficients is established. Considering the interactions among neurons, electrical effect induced by TMS therapy, and random effect, the probability density function with respect to the firing rates of neurons of the above equation is constructed, which satisfies a static Fokker–Planck equation with quasi-periodic coefficients. Hence, different clinical TMS therapies are discussed numerically by setting different parameters, such as the coupling strengths, the intensity, frequency, initial phase, phase difference of the electric field. In addition, a functional connectivity matrix related to the adjacency matrix with variable coupling strengths based on data from a real brain network is constructed. It is shown that the proper coupling strengths and the electric field parameters are crucial for TMS therapy. The methods include Kolmogorov–Arnold–Moser (KAM) theory, numerical analysis, and data analysis, having interdisciplinary characteristics. The result is original, which may be applied to TMS combined with drug therapy and the cognitive process of the brain.

Suggested Citation

  • Ren, Xiufang & Lu, Yao & Luo, Jie & Zeng, Xudong, 2024. "Response solutions for a kind of quasi-periodic forced neuron system," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:chsofr:v:179:y:2024:i:c:s0960077923013139
    DOI: 10.1016/j.chaos.2023.114411
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    1. Yinqing Li & Violeta G. Lopez-Huerta & Xian Adiconis & Kirsten Levandowski & Soonwook Choi & Sean K. Simmons & Mario A. Arias-Garcia & Baolin Guo & Annie Y. Yao & Timothy R. Blosser & Ralf D. Wimmer &, 2020. "Distinct subnetworks of the thalamic reticular nucleus," Nature, Nature, vol. 583(7818), pages 819-824, July.
    2. Yiben Xu & Xian Long & Jianfeng Feng & Pulin Gong, 2023. "Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing," Nature Human Behaviour, Nature, vol. 7(7), pages 1196-1215, July.
    3. Jianping Wu & Zhen Yan & Zhangqiang Li & Xingyang Qian & Shan Lu & Mengqiu Dong & Qiang Zhou & Nieng Yan, 2016. "Structure of the voltage-gated calcium channel Cav1.1 at 3.6 Å resolution," Nature, Nature, vol. 537(7619), pages 191-196, September.
    4. Shuangshuang Ma & Min Chen & Yihao Jiang & Xinkuan Xiang & Shiqi Wang & Zuohang Wu & Shuo Li & Yihui Cui & Junying Wang & Yanqing Zhu & Yan Zhang & Huan Ma & Shumin Duan & Haohong Li & Yan Yang & Chri, 2023. "Sustained antidepressant effect of ketamine through NMDAR trapping in the LHb," Nature, Nature, vol. 622(7984), pages 802-809, October.
    5. Lin, Hairong & Wang, Chunhua, 2020. "Influences of electromagnetic radiation distribution on chaotic dynamics of a neural network," Applied Mathematics and Computation, Elsevier, vol. 369(C).
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