Antiphase bursting related to the rhythmic motor behavior exhibits complex dynamics modulated by the inhibitory synaptic current (Isyn), especially in the presence of the hyperpolarization-activated cation current (Ih). In the present paper, the dynamics of antiphase bursting modulated by the Ih and Isyn is studied in three aspects with a theoretical model. Firstly, the Isyn and the slow Ih with strong strength are the identified to be the necessary conditions for the antiphase bursting. The dependence of the antiphase bursting on the two currents is different for low (escape mode) and high (release mode) threshold voltages (Vth) of the inhibitory synapse. Secondly, more detailed co-regulations of the two currents to induce opposite changes of the bursting period are obtained. For the escape mode, increase of the Ih induces elevated membrane potential of the silence inhibited by a strong Isyn and shortened silence duration to go beyond Vth, resulting in reduced bursting period. For the release mode, increase of the Ih induces elevated tough value of the former part of the burst modulated by a nearly zero Isyn and lengthen burst duration to fall below Vth, resulting in prolonged bursting period. Finally, the fast-slow dynamics of the antiphase bursting are acquired. Using one-and two-parameter bifurcations of the fast subsystem of a single neuron, the burst of the antiphase bursting is related to the stable limit cycle, and the silence modulated by a strong Isyn to the stable equilibrium to a certain extent. The Ih mainly modulates the dynamics within the burst and quiescent state. Furthermore, with the fast subsystem of the coupled neurons, the silence is associated with the unstable equilibrium point. The results present theoretical explanations to the changes in the bursting period and fast-slow dynamics of the antiphase bursting modulated by the Isyn and Ih, which is helpful for understanding the antiphase bursting and modulating rhythmic motor patterns.

中文翻译：

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抑制性突触和超极化激活阳离子电流调制的反相爆发动力学

与节律性运动行为相关的反相爆发表现出由抑制性突触电流调节的复杂动力学（我顺），特别是在存在超极化激活的阳离子电流的情况下（我H）。在本文中，反相爆发的动力学由调制我H和我顺并通过理论模型从三个方面进行了研究。首先，我顺和缓慢的我H强度强被认为是反相爆发的必要条件。对于低（逃逸模式）和高（释放模式）阈值电压，反相突发对两个电流的依赖性是不同的（Vth）的抑制性突触。其次，获得了两个电流的更详细的共同调节以引起突发周期的相反变化。对于逃脱模式，增加我H诱导由强抑制的沉默的膜电位升高我顺并缩短沉默时间以超越Vth，导致爆破周期缩短。对于发布模式，增加我H导致爆发前部分的坚韧值升高，调制值几乎为零我顺并延长突发持续时间以低于Vth，导致爆裂期延长。最后，获得了反相爆发的快慢动力学。利用单个神经元的快速子系统的一参数和二参数分岔，反相爆发的爆发与稳定极限环相关，并且由强调制的沉默我顺达到一定程度的稳定平衡。这我H主要调节突发状态和静态状态下的动态。此外，对于耦合神经元的快速子系统，沉默与不稳定的平衡点相关。结果对反相爆发调制的爆发周期和快慢动态的变化提供了理论解释。我顺和我H，这有助于理解反相爆发和调节节律性运动模式。