耦合振子系统中振幅包络同相同步向反相同步的转变

Amplitude envelope transition from in-phase to anti-phase synchronization in coupled oscillators system

耦合振子系统的振幅包络同步行为反映了耦合振子系统幅度与相位的相互作用.在吸引耦合神经元振子系统中引入排斥耦合作用,耦合系统的振幅包络会随着排斥耦合作用的增加从同相同步向反相同步转变.对于给定的吸引耦合神经元振子,随着引入的排斥耦合强度增加,耦合神经元振子的振幅包络之间的相位差会先从0耦合系统中的同步是由于振子之间的相互作用而使整个动力学系统趋于相同的集群动力学现象.随着研究的不断深入,增加至π,然后又由π开始减小.同时,振幅包络的幅值会随排斥耦合强度的增加先减小后增加,存在一个使振幅包络的幅度达到最小值的排斥耦合强度.吸引与排斥耦合竞争引起的振幅包络从同相同步向反相同步转变过程也可以在引入时间尺度的耦合Stuart-Landau振子中产生,具有普适性.该研究不仅可以丰富振幅包络的相关动力学研究,还有助于理解脑信息处理和传递过程.

Envelope synchronization behavior of coupled oscillator system reflects the interaction between amplitude and phase of coupled oscillator system.Introducing a repulsive coupling interaction in attractively coupled neuron oscillator system,the amplitude envelope of coupled system will transit from in-phase to anti-phase synchronization as the repulsive coupling strength increases.As a given attractively coupled strength,the phase difference between amplitude envelopes of coupled neuron oscillators increase from 0 toπand then decrease with the increment of repulsive coupling strength.Meanwhile,the amplitude of amplitude envelope will first decrease and then increase with the increment of repulsive coupling strength,and there is a repulsive coupling strength that minimized the amplitude of amplitude envelope.The transition from in-phase to anti-phase synchronization of amplitude envelope is induced by the competition of attractive and repulsive coupling can also be obtained in coupled Stuart-Landau oscillators with different time-scales.This study is not only of great significance to enrich the relevant dynamics study of amplitude envelope,but also the basis and key to study the processing and transmitting information in brain science.