论文标题
受控扰动诱导的脉冲耦合振荡器网络中的开关
Controlled Perturbation-Induced Switching in Pulse-Coupled Oscillator Networks
论文作者
论文摘要
脉搏耦合系统（例如尖峰神经网络）以吸引单位同步为组的单位同步的鞍座周期性轨道的形式表现出非平凡的不变式集合。这种轨道之间的杂斜连接可能原则上支持这些网络中的切换过程，并启用新型的神经计算。对于耦合振荡器的小型网络，我们在这里调查了哪些条件以及系统对称性如何强制执行或禁止通过扰动引起的某些切换过渡。对于五个振荡器的网络，我们得出了明确的过渡规则，该规则对于两个群集对称性，偏离了与振荡器已知的旋转器，并及时连续耦合。第三个对称性产生的杂斜网络由所有不稳定吸引子组成的集合和它们之间的连接组成。我们的结果表明，脉冲耦合系统可以可靠地生成符合特定过渡规则的复杂时空模式的明确定义的集合。我们简要讨论使用尖峰神经系统计算的可能影响。
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may in principle support switching processes in those networks and enable novel kinds of neural computations. For small networks of coupled oscillators we here investigate under which conditions and how system symmetry enforces or forbids certain switching transitions that may be induced by perturbations. For networks of five oscillators we derive explicit transition rules that for two cluster symmetries deviate from those known from oscillators coupled continuously in time. A third symmetry yields heteroclinic networks that consist of sets of all unstable attractors with that symmetry and the connections between them. Our results indicate that pulse-coupled systems can reliably generate well-defined sets of complex spatiotemporal patterns that conform to specific transition rules. We briefly discuss possible implications for computation with spiking neural systems.
