Enhancement of dynamical robustness in a mean-field coupled network through self-feedback delay

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.