中国物理B ›› 2021, Vol. 30 ›› Issue (5): 50502-050502.doi: 10.1088/1674-1056/abcfa9

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Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns

Ben Cao(曹奔)1, Huaguang Gu(古华光)1,†, and Yuye Li(李玉叶)2,3   

  1. 1 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China;
    2 College of Mathematics and Computer Science, Chifeng University, Chifeng 024000, China;
    3 Institute of Applied Mathematics, Chifeng University, Chifeng 024000, China
  • 收稿日期:2020-10-05 修回日期:2020-10-30 接受日期:2020-12-02 出版日期:2021-05-14 发布日期:2021-05-14
  • 通讯作者: Huaguang Gu E-mail:guhuaguang@tongji.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11872276 and 11762001) and the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region, China (Grant No. NJYT-20-A09).

Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns

Ben Cao(曹奔)1, Huaguang Gu(古华光)1,†, and Yuye Li(李玉叶)2,3   

  1. 1 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China;
    2 College of Mathematics and Computer Science, Chifeng University, Chifeng 024000, China;
    3 Institute of Applied Mathematics, Chifeng University, Chifeng 024000, China
  • Received:2020-10-05 Revised:2020-10-30 Accepted:2020-12-02 Online:2021-05-14 Published:2021-05-14
  • Contact: Huaguang Gu E-mail:guhuaguang@tongji.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11872276 and 11762001) and the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region, China (Grant No. NJYT-20-A09).

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摘要： In traditional viewpoint, excitatory modulation always promotes neural firing activities. On contrary, the negative responses of complex bursting behaviors to excitatory self-feedback mediated by autapse with time delay are acquired in the present paper. Two representative bursting patterns which are identified respectively to be “Fold/Big Homoclinic” bursting and “Circle/Fold cycle” bursting with bifurcations are studied. For both burstings, excitatory modulation can induce less spikes per burst for suitable time delay and strength of the self-feedback/autapse, because the modulation can change the initial or termination phases of the burst. For the former bursting composed of quiescent state and burst, the mean firing frequency exhibits increase, due to that the quiescent state becomes much shorter than the burst. However, for the latter bursting pattern with more complex behavior which is depolarization block lying between burst and quiescent state, the firing frequency manifests decrease in a wide range of time delay and strength, because the duration of both depolarization block and quiescent state becomes long. Therefore, the decrease degree of spike number per burst is larger than that of the bursting period, which is the cause for the decrease of firing frequency. Such reduced bursting activity is explained with the relations between the bifurcation points of the fast subsystem and the bursting trajectory. The present paper provides novel examples of paradoxical phenomenon that the excitatory effect induces negative responses, which presents possible novel modulation measures and potential functions of excitatory self-feedback/autapse to reduce bursting activities.

关键词: bifurcation, bursting, excitatory autapse, time delay

Abstract: In traditional viewpoint, excitatory modulation always promotes neural firing activities. On contrary, the negative responses of complex bursting behaviors to excitatory self-feedback mediated by autapse with time delay are acquired in the present paper. Two representative bursting patterns which are identified respectively to be “Fold/Big Homoclinic” bursting and “Circle/Fold cycle” bursting with bifurcations are studied. For both burstings, excitatory modulation can induce less spikes per burst for suitable time delay and strength of the self-feedback/autapse, because the modulation can change the initial or termination phases of the burst. For the former bursting composed of quiescent state and burst, the mean firing frequency exhibits increase, due to that the quiescent state becomes much shorter than the burst. However, for the latter bursting pattern with more complex behavior which is depolarization block lying between burst and quiescent state, the firing frequency manifests decrease in a wide range of time delay and strength, because the duration of both depolarization block and quiescent state becomes long. Therefore, the decrease degree of spike number per burst is larger than that of the bursting period, which is the cause for the decrease of firing frequency. Such reduced bursting activity is explained with the relations between the bifurcation points of the fast subsystem and the bursting trajectory. The present paper provides novel examples of paradoxical phenomenon that the excitatory effect induces negative responses, which presents possible novel modulation measures and potential functions of excitatory self-feedback/autapse to reduce bursting activities.

Key words: bifurcation, bursting, excitatory autapse, time delay

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
87.19.lg (Synapses: chemical and electrical (gap junctions))