The role of counter-rotating oscillators in an ensemble of coexisting co-and counter-rotating oscillators is examined by increasing the proportion of the latter. The phenomenon of aging transition was identified at a critical value of the ratio of the counter-rotating oscillators, which was otherwise realized only by increasing the number of inactive oscillators to a large extent. The effect of the mean-field feedback strength in the symmetry preserving coupling is also explored. The parameter space of aging transition was increased abruptly even for a feeble decrease in the feedback strength and subsequently aging transition was observed at a critical value of the feedback strength surprisingly without any counter-rotating oscillators. Further, the study was extended to symmetry breaking coupling using conjugate variables and it was observed that the symmetry breaking coupling can facilitating the onset of aging transition even in the absence of counter-rotating oscillators and for the unit value of the feedback strength. In general, the parameter space of aging transition was found to increase by increasing the frequency of oscillators and by increasing the proportion of the counter-rotating oscillators in both the symmetry preserving and symmetry breaking couplings. Further, the transition from oscillatory to aging transition occurs via a Hopf bifurcation, while the transition from aging transition to oscillation death state emerges via Pitchfork bifurcation. Analytical expressions for the critical ratio of the counterrotating oscillators are deduced to find the stable boundaries of the aging transition.Aging is a kind of deterioration which occurs in diverse complex systems. It is evident from our daily life that living organisms (and its efficiency) degrade as it becomes older. For instance, Alzheimer's disease is an example of a cause of failure of neurons due to the aging process. In this context, the phenomenon of aging transition was reported in an ensemble of oscillators by increasing the proportion of inactive oscillator [25][26][27][28][29][30] . In the present work, we show that even an appropriate proportion of counter-rotating oscillators in an ensemble of coexisting co-and counterrotating oscillator is capable of inducing the phenomenon of aging transition. Further, we find that either the meanfield feedback or the symmetry breaking coupling alone can facilitate the onset of the aging transition.
We investigate the effect of symmetry breaking couplings on the macroscopic dynamical behavior of an ensemble of globally coupled active and inactive oscillators. Conjugate coupling among the ensemble and the weighted coupling within the active and inactive groups introduces the asymmetry. Large values of the global coupling strength facilitate the onset of the phenomenon of aging transition, thereby deteriorating the macroscopic oscillatory behavior. We find that the natural frequency of oscillation favors the onset of the aging transition even in the presence of a large proportion of the active oscillators because of the broken symmetry. Further the ratio of the intra-group (weighted) couplings plays a nontrivial role in determining the dynamical behaviors and their transitions. It is also observed that even a feeble change in the simple feedback factor in the coupling facilitates the counterintuitive effect of preserving the macroscopic oscillatory nature of the ensemble, comprising completely inactive oscillators, in the entire parameter space where the ensemble suffered the aging transition.
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