Global multistability and mechanisms of a memristive autapse-based Filippov Hindmash-Rose neuron model
Global multistability and mechanisms of a memristive autapse-based Filippov Hindmash-Rose neuron model
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DOI：
10.1016/j.chaos.2022.112281
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Chenghua Gao;Shuai Qiao;Xinlei An
中科院分区：
文献类型：
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作者：
Chenghua Gao;Shuai Qiao;Xinlei An
神经系统中的电磁感应可以通过记忆自适应来模拟，记忆自适应在调节生理功能方面起着关键作用。提出了以膜电位为阈值的非连续控制策略。在此基础上，通过阈值控制策略改进忆阻自适应，建立了四维Filippov Hindmash-Rose（HR）神经元模型。讨论了两个子系统的存在性、稳定性和分岔条件，并借助双参数分岔分析和全局吸引盆进一步揭示了系统的分岔区域及其内在机制.随后，复杂的滑模动力学的模型，包括滑动段，各种平衡点，滑动分叉进行了分析，通过微分包含理论。大量的数值结果表明，该阈值策略导致了滑动爆发、滑动极限环和共存吸引子等现象的出现，并基于快慢变量剖分方法揭示了阈值策略反馈下滑动电活动、模式转换和多稳定性的机理.最后，证实了高斯白色噪声诱导多稳态演化模式和随机分岔的内在机制。所得结果将有助于功能神经网络的进一步设计，并为智力残疾患者的治疗提供潜在的指导。
Electromagnetic induction in the nervous system can be emulated by memristive autapses, which plays a critical role in regulating physiological functions. A discontinuous control strategy has been proposed by taking membrane potential as the threshold. Accordingly, a four-dimensional Filippov Hindmash-Rose (HR) neuron model is established by improving the memristive autapse with the threshold control strategy. The existence, stability, and bifurcation conditions of the two subsystems are discussed, and the bistable regions and their internal mechanism are further revealed with the help of two-parameter bifurcation analysis and global basins of attraction. Subsequently, the complex sliding mode dynamics of the model including sliding segments, various equilibrium points, and sliding bifurcations are analyzed via differential inclusions theory. Then, extensive numerical results exhibit that the proposed threshold strategy leads to the occurrence of sliding bursting, sliding limit cycle and coexisting attractors, and so on. Moreover, the mechanism of sliding electric activities, mode transition, and multistability under the threshold strategy feedback is revealed based on the fast-slow variable dissection method. Finally, the internal mechanism of multistable evolutionary patterns and stochastic bifurcations induced by Gaussian white noise is confirmed. The obtained results will contribute to the further design of functional neural networks and provide potential guidance for the treatment of patients with intellectual disabilities.