Ren Quansheng, Kolwankar Kiran M, Samal Areejit, Jost Jürgen
School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056103. doi: 10.1103/PhysRevE.86.056103. Epub 2012 Nov 6.
We study the interplay of topology and dynamics in a neural network connected with spike-timing-dependent plasticity (STDP) synapses. Stimulated with periodic spike trains, the STDP-driven network undergoes a synaptic pruning process and evolves to a residual network. We examine the variation of topological and dynamical properties of the residual network by varying two key parameters of STDP: synaptic delay and the ratio between potentiation and depression. Our extensive numerical simulations of the leaky integrate-and-fire model show that there exists two regions in the parameter space. The first corresponds to fixed-point configurations, where the distribution of peak synaptic conductances and the firing rate of neurons remain constant over time. The second corresponds to oscillating configurations, where both topological and dynamical properties vary periodically, which is a result of a fixed point becoming a limit cycle via a Hopf bifurcation. This leads to interesting questions regarding the implications of these rhythms in the topology and dynamics of the network for learning and cognitive processing.
我们研究了与基于尖峰时间依赖可塑性（STDP）突触相连的神经网络中拓扑结构与动力学之间的相互作用。用周期性尖峰序列进行刺激时，由STDP驱动的网络会经历突触修剪过程，并演变成一个残差网络。我们通过改变STDP的两个关键参数：突触延迟以及增强与抑制之间的比率，来研究残差网络的拓扑和动力学特性的变化。我们对泄漏积分发放模型进行的大量数值模拟表明，在参数空间中存在两个区域。第一个区域对应于定点配置，其中峰值突触电导的分布和神经元的发放率随时间保持恒定。第二个区域对应于振荡配置，其中拓扑和动力学特性都会周期性变化，这是一个定点通过霍普夫分岔变成极限环的结果。这引发了一些有趣的问题，即这些节律在网络的拓扑和动力学中对于学习和认知处理的意义。
