Time-delay effects on the aging transition in a population of coupled oscillators

Abstract

We investigate the influence of time-delayed coupling on the nature of the aging transition in a system of coupled oscillators that have a mix of active and inactive oscillators, where the aging transition is defined as the gradual loss of collective synchrony as the proportion of inactive oscillators is increased. We start from a simple model of two time-delay coupled Stuart-Landau oscillators that have identical frequencies but are located at different distances from the Hopf bifurcation point. A systematic numerical and analytic study delineates the dependence of the critical coupling strength (at which the system experiences total loss of synchrony) on time delay and the average distance of the system from the Hopf bifurcation point. We find that time delay can act to facilitate the aging transition by lowering the threshold coupling strength for amplitude death in the system. We then extend our study to larger systems of globally coupled active and inactive oscillators including an infinite system in the thermodynamic limit. Our model system and results can provide a useful paradigm for understanding the functional robustness of diverse physical and biological systems that are prone to aging transitions.

Enhancing dynamical robustness in aging networks of coupled nonlinear oscillators

“…The AT is impossible if the coupling strength is large enough once α deviating from unity. The above observation suggests that the large coupling strength is favorable for a dynamical robustness of the network against aging if α < 1, which is sharp contrast to the case of α = 1, where the strong coupling strength has been reported to spoil the robustness of the network's activity [6,[14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”

“…One peculiar and curious aspect of the AT is that the strong diffusive coupling spoils the robustness of dynamic activity of coupled systems commonly made in refs. [6,[14][15][16][17][18][19][20][21][22][23][24][25][26][27], which is in stark contrast with the intuitive understanding of its effect in facilitating the coherent behaviors of systems [28,29].…”

“…The coupling type in eq. 1is different from that adopted in the previous studies about AT in networks of diffusively coupled oscillators [6,[14][15][16][17][18][19][20][21][22][23][24][25][26][27], as a new feedback factor α (0 ≤ α ≤ 1) is introduced in the normal form of diffusive coupling. In physics, the parameter α plays a role to control the degree of diffusion, which recovers to symmetrical diffusion for α = 1 and direct coupling for α = 0.…”

“…The magnitude of p c can be regarded as an index of the dynamical robustness of the coupled networks; the higher the value of p c , the more dynamically robust the network is. Employing this index, the robustness of dynamic activity in networks of diffusively coupled oscillators can be quantitatively characterized, which has been intensively discussed during the last decade [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. One peculiar and curious aspect of the AT is that the strong diffusive coupling spoils the robustness of dynamic activity of coupled systems commonly made in refs.…”

Bifurcation and scaling at the aging transition boundary in globally coupled excitable and oscillatory units

“…Although there are quite a few achievements in both theory and experiment concerning the dynamics of such systems [6,7], there are not so many studies about the robustness of their dynamic activity against the deterioration of constituent oscillators [8][9][10][11][12][13][14][15][16][17]. Such a study started nearly a decade ago, in which the concept of "aging," defined as an increase in the ratio of inactive oscillators (i.e., damped oscillators in a generalized sense) in the system, was proposed and led to a discovery of an aging transition, namely, a transition from a dynamic state to a static one caused by the aging [8].…”