Enhancing dynamical robustness in aging networks of coupled nonlinear oscillators

Abstract

We propose an effective method to enhance the dynamical robustness of networks of diffusively coupled oscillators experiencing aging transition. By introducing a new control parameter into the normal diffusive coupling, we demonstrate that the dynamical robustness of coupled oscillator networks can be efficiently improved by enhancing the tolerance of dynamic activity in the network to inactivation or deterioration of the individual oscillators. Even a tiny deviation from the normal diffusive coupling greatly strengthens the robustness of networks. Particularly, the strong coupling in our scheme is shown to be in favor of the dynamic activity, which is in sharp contrast to the normal form of diffusive coupling with the tendency to spoil the dynamical robustness. Our proposed approach serves as a rather simple and efficient way to recover dynamic activity in networks of diffusively coupled oscillators that has been lost due to some inactivated or damaged oscillator components.

Symmetry breaking induced tipping to aging

“…Recent activities on aging are centered at enhancing the robustness of the macroscopic oscillatory state despite the presence of a large fraction of inactive oscillators. For instance, several methods such as introducing auxiliary systems in the coupling [11], introducing a simple limiting factor that limits the diffusive interaction [12], incorporating large variance of the asymmetry parameter [11], employing adaptive coupling such as low-pass filters [13], introducing asymmetry coupling among the populations [11], and allowing normal and uniform random errors in the Hopf bifurcation parameters [14], etc. have been shown to increase the robustness of the macroscopic oscillatory state over a large range of coupling strength and even shown to prevent the onset of aging in several scenarios despite the presence of a large fraction of the inactive oscillators.…”

A Chimera Oscillatory State in a Globally Delay-Coupled Oscillator Network

“…To investigate the collective behavior, the model of coupled nonlinear oscillators is simple but powerful [1][2][3][4][5][6][7][8]. Aging transition (AT), one of the significant collective behaviors, has been concerned by physical researchers and studied in different dynamical models [9][10][11][12][13]. e AT phenomenon appears usually in a damaged network, in which some active oscillators lose their activity and become a mixed network made up with selfoscillatory and non-self-oscillatory oscillators.…”

“…To avoid the aging effect, many strategies are presented. For example, the aging effect can be eliminated by regulating a control parameter in the normal diffusive coupling, and the dynamical robustness of damaged networks can be efficiently enhanced [11]. A scheme based on external feedback has been put forward, and the method can efficiently protect oscillatory behavior in the aging networks of active and inactive elements [17].…”

Dangerous Aging Transition in a Network of Coupled Oscillators

“…If this degradation reaches a certain critical point, the regular functioning of such systems may hamper and face severe disruption. This emergent behaviour is described as aging transition and is an active area of research [4][5][6][7][8][9][10][11][12][13][14] . The aging transitions might cause catastrophic effects in many natural and real-world systems such as metapopulation dynamics in ecology, neuronal dynamics in brain, cardiac oscillations, and powergrid network [15][16][17][18] .…”