负反馈诱发神经电振荡的反常现象的复杂动力学  

THE COMPLEX DYNAMICS OF ABNORMAL PHENOMENON OF NEURAL ELECTRONIC OSCILLATIONS INDUCED BY NEGATIVE FEEDBACK

作　　者：蓝昱群 关利南 古华光 Lan Yuqun;Guan Linan;Gu Huaguang(School of Aerospace and Applied Mechanics, Tongji University, Shanghai 200092, China)

机构地区：[1]同济大学航空航天与力学学院

出　　处：《力学学报》2019年第4期1122-1133,共12页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金项目(11872276,11572225);国家级大学生创新创业训练计划(G201845001)资助

摘　　要：传统观念认为,负反馈容易使系统达到稳定平衡点而正反馈容易引起振荡.本研究基于神经元理论模型,提出了负反馈可以诱发稳定平衡点–也就是静息–变为振荡–也就是放电的新观点.在Hopf分岔点附近,作用在静息上的一次足够大的负向脉冲电流的抑制性刺激,能够引起一个动作电位及随后的衰减振荡的后电位;而能够在后电位上诱发出动作电位的负脉冲电流强度阈值也是衰减振荡的.在模型中,引入具有时滞(τ)的负反馈来模拟抑制性自突触,一个动作电位诱发的负反馈自突触电流会作用到比动作电位延迟τ的后电位上.随时滞增加,能够诱发出放电的负反馈增益强度阈值呈现出具有衰减振荡特点的类似多重相干共振的特性,衰减振荡的周期与电流阈值曲线的周期以及分岔点附近的放电周期相关.另外,负反馈还能诱发出放电与静息共存的复杂行为.本研究的结果不仅揭示了负反馈的新的反常调控作用,还有助于理解在现实神经系统中存在的慢抑制性自突触的潜在功能.In traditional viewpoint, it is easy to achieve stable equilibrium for a system with negative feedback and stable oscillations for a system with positive feedback. In the present investigation of the nonlinear neural system, a novel viewpoint that negative feedback can induce stable equilibrium, i.e. the resting state, changed to oscillations, i.e.firing, is proposed. In a theoretical neuron model, inhibitory stimulation mediated by the negative impulsive current with enough strength can induce an action potential from the resting state near a Hopf bifurcation point and the after-potential with damping oscillations following the action potential. The strength threshold of the second negative impulsive current applied within the after-potential to evoke the second action potential exhibits damping oscillations as well with respect to the application phase of the current. After introducing negative feedback with time delay(τ) into the theoretical model to simulate the inhibitory autapse, the negative feedback current induced by an action potential is applied at the phase τ of the after-potential following the action potential. The negative feedback gain threshold to induce firing from the resting state exhibits characteristics of damping oscillations with increasing time delay corresponding to application phase of the current, which resembles the time delay induced-multiple coherence resonances. The oscillation period is associated with the period of strength threshold curve of the second impulsive current to evoke the second action potential from after-potential and the period of the firing near the Hopf bifurcation. Furthermore, the negative feedback can also induce complex dynamics such as the coexistence of the firing and resting state. The results of the present paper not only present a novel modulation effect of the negative feedback, which is a contrast to the tradition viewpoint, but also are helpful for understanding the potential functions of slow inhibitory autapse that can induce negative impulsive cu

关 键 词：HOPF分岔 神经放电 负反馈 时滞 共存 

分 类 号：O322[理学—一般力学与力学基础] Q424[理学—力学]