Asymmetric feedback enhances rhythmicity in damaged systems of coupled fractional oscillators

Collective oscillatory behavior plays a key role in proper functioning of various coupled systems in the real world. However, a variety of damages or deterioration may come up inevitably in coupled systems that can affect macroscopic activity of the entire system. Therefore, we need to provide some remedies to against such aging. To do this, a coupled fractional oscillators model composed of active and inactive oscillators is adopted to demonstrate this scenario. We introduce an asymmetric feedback into damaged fractional system to enhance its rhythmicity. Our results suggest that the critical ratio of inactive oscillators depends on the asymmetric feedback monotonously. Accordingly, one can enhance dynamical robustness via reducing the asymmetric feedback. It is found that strong coupling is in favor of the dynamical activity of coupled system with asymmetric coupling, which is in contrast to the normal diffusive interaction that shows the tendency to spoil the dynamical robustness. An astonishing phenomenon has been found that coupled fractional oscillators system possesses the oscillation even all the oscillators turn to inactive when asymmetric feedback less than a critical value associated with fractional derivative. Moreover, we investigate the effects of asymmetric feedback on the delay-coupled fractional oscillators system and show that the reduction in asymmetric feedback can enhance dynamical robustness as well. Remarkably, the critical ratio at which aging transition occurs depends unmonotonously on the time delay, which implies that the delay-coupled fractional systems possess the weakest dynamical robustness at a certain level of time delay in the presence of asymmetric feedback.