具有间隙连接的两个耦合 HR 神经元的平衡分析与相位同步。
Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction.
机构信息
School of Science, Nanjing University of Science and Technology, Nanjing, 210094 China.
Department of Dynamics and Control, Beihang University, Beijing, 100191 China.
出版信息
Cogn Neurodyn. 2013 Apr;7(2):121-31. doi: 10.1007/s11571-012-9222-0. Epub 2012 Sep 28.
The properties of equilibria and phase synchronization involving burst synchronization and spike synchronization of two electrically coupled HR neurons are studied in this paper. The findings reveal that in the non-delayed system the existence of equilibria can be turned into intersection of two odd functions, and two types of equilibria with symmetry and non-symmetry can be found. With the stability and bifurcation analysis, the bifurcations of equilibria are investigated. For the delayed system, the equilibria remain unchanged. However, the Hopf bifurcation point is drastically affected by time delay. For the phase synchronization, we focus on the synchronization transition from burst synchronization to spike synchronization in the non-delayed system and the effect of coupling strength and time delay on spike synchronization in delayed system. In addition, corresponding firing rhythms and spike synchronized regions are obtained in the two parameters plane. The results allow us to better understand the properties of equilibria, multi-time-scale properties of synchronization and temporal encoding scheme in neuronal systems.
本文研究了两个电耦合 HR 神经元的爆发同步和尖峰同步涉及的平衡态和相位同步的性质。研究结果表明，在非时滞系统中，平衡态的存在可以转化为两个奇函数的交点，并且可以找到具有对称性和非对称性的两种平衡态。通过稳定性和分岔分析，研究了平衡态的分岔。对于时滞系统，平衡态保持不变。然而，时滞对平衡点的 Hopf 分岔点有很大的影响。对于相位同步，我们关注的是在非时滞系统中从爆发同步到尖峰同步的同步转变，以及耦合强度和时滞对延迟系统中尖峰同步的影响。此外，在两个参数平面上获得了相应的发射节律和尖峰同步区域。这些结果使我们能够更好地理解神经元系统中平衡态、同步的多时间尺度性质和时间编码方案的性质。
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