Embedding the dynamics of a single delay system into a feed-forward ring.
Embedding the dynamics of a single delay system into a feed-forward ring.
复制标题
DOI：
10.1103/physreve.96.042217
复制
发表时间：
2017-09
期刊：
影响因子：
--
通讯作者：
V. Klinshov;D. Shchapin;S. Yanchuk;M. Wolfrum;O. D’Huys;V. Nekorkin
中科院分区：
文献类型：
--
作者：
V. Klinshov;D. Shchapin;S. Yanchuk;M. Wolfrum;O. D’Huys;V. Nekorkin
我们研究了具有延迟自反馈的单个振荡器的动力学和这样的振荡器的前馈环之间的关系，其中每个单元以与自反馈情况相同的方式耦合到其下一个邻居。我们证明了延迟振子的周期解会在相应的环中产生具有不同波数的旋转波族。特别地，如果对于单个振荡器的周期解是谐振的延迟，它可以被嵌入到一个环的瞬时耦合。我们发现了几种情况下，一个周期解的稳定性的单一单位可以相关的稳定性相应的旋转波的环。作为一个具体的例子，我们演示了如何复杂的分叉的情况下，同时出现的多抖动的解决方案可以从一个单一的振荡器与延迟脉冲反馈到多抖动旋转波在一个足够大的环振荡器与瞬时脉冲耦合。最后，我们提出了一个实验实现这种动力学现象的FitzHugh-Nagumo型耦合电子电路系统。
We investigate the relation between the dynamics of a single oscillator with delayed self-feedback and a feed-forward ring of such oscillators, where each unit is coupled to its next neighbor in the same way as in the self-feedback case. We show that periodic solutions of the delayed oscillator give rise to families of rotating waves with different wave numbers in the corresponding ring. In particular, if for the single oscillator the periodic solution is resonant to the delay, it can be embedded into a ring with instantaneous couplings. We discover several cases where the stability of a periodic solution for the single unit can be related to the stability of the corresponding rotating wave in the ring. As a specific example, we demonstrate how the complex bifurcation scenario of simultaneously emerging multijittering solutions can be transferred from a single oscillator with delayed pulse feedback to multijittering rotating waves in a sufficiently large ring of oscillators with instantaneous pulse coupling. Finally, we present an experimental realization of this dynamical phenomenon in a system of coupled electronic circuits of FitzHugh-Nagumo type.