School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, People's Republic of China.
Chaos. 2011 Mar;21(1):013127. doi: 10.1063/1.3565027.
We investigate the chaotic phase synchronization in a system of coupled bursting neurons in small-world networks. 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 phase synchronization is largely facilitated by a large fraction of shortcuts, but saturates when it exceeds a critical value. We also study the external chaotic phase synchronization of bursting oscillators in the small-world network by a periodic driving signal applied to a single neuron. It is demonstrated that there exists an optimal small-world topology, resulting in the largest peak value of frequency locking interval in the parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this interval increases with the driving amplitude, but decrease rapidly with the network size. We infer that the externally applied driving parameters outside the frequency locking region can effectively suppress pathologically synchronized rhythms of bursting neurons in the brain.
我们研究了小世界网络中耦合爆发神经元系统中的混沌相位同步。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，它们表现为异步。结果表明，相位同步很大程度上得益于短程连接的大量存在，但当它超过临界值时会饱和。我们还通过施加于单个神经元的周期性驱动信号研究了小世界网络中爆发振荡器的外部混沌相位同步。结果表明，存在一个最优的小世界拓扑结构，在爆发同步得以维持的参数平面中，导致最大的锁频间隔峰值。即使施加外部驱动，该间隔的宽度也会随着驱动幅度的增加而增加，但随着网络规模的减小而迅速减小。我们推断，在锁频区域之外的外部施加的驱动参数可以有效地抑制大脑中爆发神经元的病理性同步节律。
