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Symmetry breaking-induced state-dependent aging and chimera-like death state
Nonlinear Dynamics ( IF 5.6 ) Pub Date : 2020-06-30 , DOI: 10.1007/s11071-020-05766-5
I. Gowthaman , K. Sathiyadevi , V. K. Chandrasekar , D. V. Senthilkumar

Aging transition refers to the manifestation of the homogeneous steady state beyond a critical ratio of the inactive oscillators in a network of active and inactive oscillators. In contrast, symmetry breaking in coupled dynamical systems always results in heterogeneous states. In this work, surprisingly, we find that the symmetry breaking coupling facilitates the onset of the homogeneous steady state among the population at the critical proportion of the inactive oscillators despite the presence of a large number of the active oscillators. Further, increase in the natural frequency of the oscillation and the number of the inactive oscillators are conducive to the onset of the aging transition. Interestingly, chimera-like death state is observed in the study related to the aging transition for the first time in the literature in addition to the actual chimera death states among the active oscillator for the random initial conditions. The critical curves corresponding to the stability of the aging transition and the chimera-like death states are deduced, which agrees perfectly with the simulation results. Even a feeble decrease in the feedback factor in the coupling destabilizes the stable aging state thereby facilitating the oscillatory state in the entire parameter space despite the presence of a large proportion of the inactive oscillators increasing the robustness of the network against disorders.



中文翻译:

对称断裂诱导的状态依赖性衰老和嵌合体样死亡状态

老化过渡是指在有源和无源振荡器网络中,超过无源振荡器的临界比的均匀稳态的表现。相反,耦合动力系统中的对称破坏总是导致异质状态。令人惊讶地,在这项工作中,我们发现尽管存在大量的有源振荡器,但对称断开耦合促进了在非有源振荡器的临界比例下总体中均匀稳态的开始。此外,振荡固有频率的增加和无效振荡器的数量有利于老化过渡的开始。有趣的是 除了随机初始条件下的有源振荡器中的实际嵌合体死亡状态外,该文献首次在与衰老过渡有关的研究中观察到了类似嵌合体的死亡状态。推导了对应于老化转变的稳定性和类似嵌合体死亡状态的临界曲线,与仿真结果完全吻合。尽管存在很大比例的无源振荡器,但即使耦合中反馈因子的微不足道地降低,稳定的老化状态也会不稳定,从而有利于整个参数空间中的振荡状态,从而提高了网络抗干扰的鲁棒性。推导了对应于老化转变的稳定性和类似嵌合体死亡状态的临界曲线,与仿真结果完全吻合。尽管存在很大比例的无源振荡器,但即使耦合中反馈因子的微不足道地降低,稳定的老化状态也会不稳定,从而有利于整个参数空间中的振荡状态,从而提高了网络抗干扰的鲁棒性。推导了对应于老化转变的稳定性和类似嵌合体死亡状态的临界曲线,与仿真结果完全吻合。尽管存在很大比例的无源振荡器,但即使耦合中反馈因子的微不足道地降低,稳定的老化状态也会不稳定,从而有利于整个参数空间中的振荡状态,从而提高了网络抗干扰的鲁棒性。

更新日期:2020-06-30
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