Post-canard symmetry breaking and other exotic dynamic behaviors in identical coupled chemical oscillators
Post-canard symmetry breaking and other exotic dynamic behaviors in identical coupled chemical oscillators
复制标题
相同耦合化学振荡器中的后鸭对称性破缺和其他奇异的动态行为
DOI：
10.1103/physreve.101.042222
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发表时间：
2020
影响因子：
2.4
通讯作者：
Epstein, Irving R.
中科院分区：
文献类型：
--
作者：
Awal, Naziru M.;Epstein, Irving R.
我们分析了两个相同的化学振子通过慢变量的扩散耦合的模型。当参数变化时，单个振荡器经历鸭式爆炸——在很小的参数区间内从小振幅、近谐振荡过渡到大振幅、弛豫振荡。在耦合系统中，如果两个振子具有相同的初始条件，则两个振子保持同步，并表现出与单振子相同的鸭式行为。如果振子最初是分开的，那么在鸭翼区域内，它们会表现出各种复杂的行为，包括间歇尖峰、混合模式振荡和准周期性。参数的进一步变化导致返回到同步的大振幅振荡，随后是鸭后对称破断，其中一个振荡器显示出小振幅，复杂的行为（混合模式振荡，准周期性，混沌，…），而另一个基本上经历周期性的大振幅行为，类似于主从场景。我们通过查看几种修改后的耦合方案来分析这种行为的起源。
We analyze a model of two identical chemical oscillators coupled through diffusion of the slow variable. As a parameter is varied, a single oscillator undergoes a canard explosion—a transition from small amplitude, nearly harmonic oscillations to large-amplitude, relaxation oscillations over a very small parameter interval. In the coupled system, if the two oscillators have the same initial conditions, then the oscillators remain synchronized and exhibit the same canard behavior observed for the single oscillator. If the oscillators are separated initially, then in the region of the canard they display a variety of complex behaviors, including intermittent spiking, mixed-mode oscillation, and quasiperiodicity. Further variation of the parameter leads to a return to synchronized large-amplitude oscillation followed by a post-canard symmetry-breaking, in which one oscillator shows small-amplitude, complex behavior (mixed-mode oscillation, quasiperiodicity, chaos,...) while the other undergoes essentially periodic large amplitude behavior, resembling a master-slave scenario. We analyze the origins of this behavior by looking at several modified coupling schemes.