School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, People's Republic of China.
Chaos. 2011 Dec;21(4):043125. doi: 10.1063/1.3660327.
We investigate the onset of chaotic phase synchronization of bursting oscillators in a modular neuronal network of small-world subnetworks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that this bursting synchronization transition can be induced not only by the variations of inter- and intra-coupling strengths but also by changing the probability of random links between different subnetworks. We also analyze the effect of external chaotic phase synchronization of bursting behavior in this clustered network by an external time-periodic signal applied to a single neuron. Simulation results demonstrate a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this synchronization region increases with the signal amplitude and the number of driven neurons but decreases rapidly with the network size. Considering that the synchronization of bursting neurons is thought to play a key role in some pathological conditions, the presented results could have important implications for the role of externally applied driving signal in controlling bursting activity in neuronal ensembles.
我们研究了小世界子网模块神经元网络中爆发振荡器混沌相位同步的开始。在耦合振荡器的爆发时间尺度上发生了向相互相位同步的转变，而在尖峰时间尺度上，它们表现出异步。结果表明，这种爆发同步转变不仅可以通过改变内外耦合强度来诱导，还可以通过改变不同子网之间随机链路的概率来诱导。我们还通过施加到单个神经元的外部时变信号来分析外部混沌相位同步对该聚类网络中爆发行为的影响。仿真结果表明，在驱动参数平面上存在一个频率锁定舌，其中即使存在外部驱动，爆发同步也能保持。该同步区域的宽度随着信号幅度和驱动神经元数量的增加而增加，但随着网络规模的迅速减小。考虑到爆发神经元的同步被认为在某些病理条件下起着关键作用，因此所提出的结果可能对外部施加的驱动信号在控制神经元集合中的爆发活动方面具有重要意义。
