School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695 551, India.
Department of Physics, Bankura University, Bankura 722 155, West Bengal, India.
Phys Rev E. 2019 Nov;100(5-1):052212. doi: 10.1103/PhysRevE.100.052212.
Mean-field diffusive coupling was known to induce the phenomenon of quenching of oscillations even in identical systems, where the standard diffusive coupling (without mean-field) fails to do so [Phys. Rev. E 89, 052912 (2014)PLEEE81539-375510.1103/PhysRevE.89.052912]. In particular, the mean-field diffusive coupling facilitates the transition from amplitude to oscillation death states and the onset of a nontrivial amplitude death state via a subcritical pitchfork bifurcation. In this paper, we show that an adaptive coupling using a low-pass filter in both the intrinsic and extrinsic variables in the coupling is capable of inducing the counterintuitive phenomenon of reviving of oscillations from the death states induced by the mean-field coupling. In particular, even a weak filtering of the extrinsic (intrinsic) variable in the mean-field coupling facilitates the onset of revival (quenching) of oscillations, whereas a strong filtering of the extrinsic (intrinsic) variable results in quenching (revival) of oscillations. Our results reveal that the degree of filtering plays a predominant role in determining the effect of filtering in the extrinsic or intrinsic variables, thereby engineering the dynamics as desired. We also extend the analysis to networks of mean-field coupled limit-cycle and chaotic oscillators along with the low-pass filters to illustrate the generic nature of our results. Finally, we demonstrate the observed dynamical transition experimentally to elucidate the robustness of our results despite the presence of inherent parameter fluctuations and noise.
平均场扩散耦合被认为会导致即使在相同的系统中也会出现振荡猝灭现象，而标准的扩散耦合（没有平均场）则无法做到这一点[Phys. Rev. E 89, 052912 (2014)PLEEE81539-375510.1103/PhysRevE.89.052912]。特别是，平均场扩散耦合通过亚临界叉形分岔促进了从振幅到振荡死亡状态的转变，并引发了非平凡的振幅死亡状态。在本文中，我们表明，在耦合中内在和外在变量中使用低通滤波器的自适应耦合能够引起由平均场耦合引起的死亡状态下的振荡复活的反直觉现象。特别是，即使是在平均场耦合中外在（内在）变量的微弱滤波也有助于引发振荡的复活（猝灭），而在平均场耦合中外在（内在）变量的强滤波则导致振荡的猝灭（复活）。我们的结果表明，滤波程度在确定外在或内在变量的滤波效果方面起着主导作用，从而按需要设计动力学。我们还将分析扩展到具有低通滤波器的平均场耦合极限环和混沌振荡器的网络中，以说明我们结果的普遍性。最后，我们通过实验证明了观察到的动力学转变，阐明了我们的结果的稳健性，尽管存在固有参数波动和噪声。
