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中国物理学会期刊

快自突触反馈诱发混合簇放电的反常变化及分岔机制

Fast autaptic feedback induced-paradoxical changes of mixed-mode bursting and bifurcation mechanism

CSTR: 32037.14.aps.70.20210208
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  • 簇放电是神经系统复杂的、多时间尺度的非线性现象, 具有多样性, 在兴奋性或抑制性作用下实现生理功能. 近期较多研究发现了与通常概念(抑制性作用引起电活动降低、兴奋性作用引起放电增强)相反的现象, 丰富了非线性科学的内涵. 本文关注于抑制性和兴奋性自突触反馈都会诱发的一类复杂的混合簇放电产生的反常现象及其分岔机制. 利用快慢变量分离, 确认了放电的复杂之处: 簇结束于极限环的鞍结分岔之后要先经过去极化阻滞才到休止期. 进一步, 揭示了该鞍结分岔在反常现象的产生中起到了关键作用. 抑制性自反馈引起了该分岔的左移导致簇的参数范围变宽, 引起簇内峰个数增多和平均放电频率增加; 而兴奋性自突触则引起该分岔右移导致电活动降低. 与其他类簇放电只在抑制性自反馈下产生反常现象和慢突触诱发的反常现象不同, 该结果给出了簇放电的反常现象的新示例及调控机制, 展示了反常现象的多样性, 有助于认识脑神经元簇放电和自反馈调控的潜在功能.

     

    Bursting is a complex multiple-time-scale nonlinear phenomenon in a nervous system and exhibits diverse patterns, which is modulated by the excitatory or inhibitory effect to achieve the physiological functions. According to the bifurcations of the fast subsystem, bursting is classified as different patterns including the mixed-mode bursting. Recently, many studies have found the paradoxical phenomena contrary to the common concept that the inhibitory effect induces the electrical activity to decrease or the excitatory effect induces the discharge activity to increase, which enriches the connotation of the nonlinear dynamics. To identify more examples of paradoxical phenomena of different bursting patterns and the underlying nonlinear mechanism, in the present study the paradoxical phenomena for the complex mixed-mode oscillations of the bursting pattern induced by the self-feedback mediated by both the inhibitory autapse and excitatory autapse and the bifurcation mechanism are acquired in the modified Morris-Lecar model. By using the fast/slow variable dissection method, the complex dynamics of the bursting is acquired, which is that the depolarization block behavior appears after the burst and before the quiescent state. The burst begins from a saddle-node bifurcation in an invariant cycle (SNIC) and terminates at a fold limit cycle (FLC) bifurcation. Furthermore, the FLC bifurcation is identified to play a key role in generating the paradoxical phenomenon. The inhibitory autapse induces the FLC bifurcation to shift leftward. However, the SNIC point remains unchanged. The change of FLC bifurcation point leads the parameter range of the burst to widen, the number of spikes per burst to become larger, and the average firing frequency to turn higher. Unlike the inhibitory autapse, the excitatory autapse induces the FLC bifurcation to shift rightward, and SNIC to be unchanged, thus reducing the bursting activity. Such results are different from those of the paradoxical phenomenon induced by the inhibitory autapse instead of excitatory autapse for the other bursting pattern and by the slow auatpse, which present a novel example and regulation mechanism of the paradoxical phenomena of the bursting patterns and show the diversity of the paradoxical phenomena, thus helping understand the potential functions of the bursting and self-feedback modulations of the brain neurons.

     

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