Burst and spike synchronization of coupled neural oscillators
Burst and spike synchronization of coupled neural oscillators
复制标题
耦合神经振荡器的突发和尖峰同步
DOI：
10.1080/14689360117083
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
K. Bräuer
中科院分区：
文献类型：
--
作者：
J. Schwarz;G. Dangelmayr;A. Stevens;K. Bräuer
神经兴奋性和从静止到振荡转变过程中的分叉在很大程度上决定了神经元的神经计算特性。Hopf分岔附近的神经元在较小的频率范围内活动，优先响应共振激励，并且易于同步。本文研究了具有非共振尖峰频率的耦合椭圆型爆发子的相互作用。爆炸行为产生于静止状态和重复发射之间的反复转换，即快速振荡行为由缓慢变化的动力学过程调制。当静态通过Hopf分岔失去稳定性，重复发射通过另一个Hopf分岔或双极限环分岔消失时，称为椭圆型爆破。通过对两个耦合爆发子的快速分系统的研究，我们得到了一个简化的方程组，该方程组允许根据频率失谐和互耦强度来描述同步和非同步振荡。我们证明了一定的“总体”耦合常数必须超过一个临界值，这取决于失谐和吸引率，以便爆发和尖峰同步可以发生。简化后的系统允许对分岔结构进行分析研究，直至协维数为3，揭示了各种固定和周期分岔，将对其进行详细分析。最后，讨论了分叉结构对脉冲和尖峰同步的影响。
Neural excitability and the bifurcations involved in transitions from quiescence to oscillations largely determine the neuro-computational properties of neurons. Neurons near Hopf bifurcation fire in a small frequency range, respond preferentially to resonant excitation, and are easily synchronized. In the present paper we study the interaction of coupled elliptic bursters with non-resonant spike frequencies. Bursting behaviour arises from recurrent transitions between a quiescent state and repetitive firing, i.e. the rapid oscillatory behaviour is modulated by a slowly varying dynamical process. Bursting is referred to as elliptic bursting when the rest state loses stability via a Hopf bifurcation and the repetitive firing disappears via another Hopf bifurcation or a double limit cycle bifurcation. By studying the fast subsystem of two coupled bursters we obtain a reduced system of equations, allowing the description of synchronized and non-synchronized oscillations depending on frequency detuning and mutual coupling strength. We show that a certain 'overall' coupling constant must exceed a critical value depending on the detuning and the attraction rates in order that burst and spike synchronization can take place. The reduced system allows an analytical study of the bifurcation structure up to codimension-3 revealing a variety of stationary and periodic bifurcations which will be analysed in detail. Finally, the implications of the bifurcation structure for burst and spike synchronization are discussed.
影响因子：
3.4
作者：
Del Negro, CA;Hsiao, CF;Garfinkel, A
通讯作者：
Garfinkel, A
影响因子：
3.5
作者：
BERTRAM, R;BUTTE, MJ;SHERMAN, A
通讯作者：
SHERMAN, A
影响因子：
2.5
作者：
MUKHERJEE, P;KAPLAN, E
通讯作者：
KAPLAN, E