Sharma Amit, Rakshit Biswambhar
Department of Physics, Central University of Rajasthan, Ajmer 305 817, India.
Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641 112, India.
Chaos. 2021 Jan;31(1):013114. doi: 10.1063/5.0015821.
The network of self-sustained oscillators plays an important role in exploring complex phenomena in many areas of science and technology. The aging of an oscillator is referred to as turning non-oscillatory due to some local perturbations that might have adverse effects in macroscopic dynamical activities of a network. In this article, we propose an efficient technique to enhance the dynamical activities for a network of coupled oscillators experiencing aging transition. In particular, we present a control mechanism based on delayed negative self-feedback, which can effectively enhance dynamical robustness in a mean-field coupled network of active and inactive oscillators. Even for a small value of delay, robustness gets enhanced to a significant level. In our proposed scheme, the enhancing effect is more pronounced for strong coupling. To our surprise even if all the oscillators perturbed to equilibrium mode were delayed negative self-feedback is able to restore oscillatory activities in the network for strong coupling strength. We demonstrate that our proposed mechanism is independent of coupling topology. For a globally coupled network, we provide numerical and analytical treatment to verify our claim. To show that our scheme is independent of network topology, we also provide numerical results for the local mean-field coupled complex network. Also, for global coupling to establish the generality of our scheme, we validate our results for both Stuart-Landau limit cycle oscillators and chaotic Rössler oscillators.
自持振荡器网络在探索许多科技领域的复杂现象中发挥着重要作用。振荡器的老化是指由于某些局部扰动而转变为非振荡状态，这些扰动可能会对网络的宏观动力学活动产生不利影响。在本文中，我们提出了一种有效的技术来增强经历老化转变的耦合振荡器网络的动力学活动。具体而言，我们提出了一种基于延迟负自反馈的控制机制，该机制可以有效地增强有源和无源振荡器的平均场耦合网络中的动力学鲁棒性。即使延迟值很小，鲁棒性也能显著提高。在我们提出的方案中，增强效果在强耦合时更为明显。令人惊讶的是，即使所有被扰动到平衡模式的振荡器，对于强耦合强度，延迟负自反馈也能够恢复网络中的振荡活动。我们证明了我们提出的机制与耦合拓扑无关。对于全局耦合网络，我们提供了数值和分析处理来验证我们的主张。为了表明我们的方案与网络拓扑无关，我们还给出了局部平均场耦合复杂网络的数值结果。此外，为了通过全局耦合来确立我们方案的通用性，我们针对斯图尔特 - 兰道极限环振荡器和混沌罗斯勒振荡器验证了我们的结果。
