Populations Of Coupled Oscillators Research Articles

Two Distinct Transitions in a Population of Coupled Oscillators with Turnover: Desynchronization and Stochastic Oscillation Quenching.

Synchronization, which is caused by mutual coupling, and turnover, which is the replacement of old components with new ones, are observed in various open systems consisting of many components. Although these phenomena can co-occur, the interplay of coupling and turnover has been overlooked. Here, we analyze coupled phase oscillators with turnover and reveal that two distinct transitions occur, depending on both coupling and turnover: desynchronization and what we name stochastic oscillation quenching. Importantly, the latter requires both the turnover and coupling to be sufficiently intense.

Tiered synchronization in coupled oscillator populations with interaction delays and higher-order interactions.

We study synchronization in large populations of coupled phase oscillators with time delays and higher-order interactions. With each of these effects individually giving rise to bistability between incoherence and synchronization via subcriticality at the onset of synchronization and the development of a saddle node, we find that their combination yields another mechanism behind bistability, where supercriticality at onset may be maintained; instead, the formation of two saddle nodes creates tiered synchronization, i.e., bistability between a weakly synchronized state and a strongly synchronized state. We demonstrate these findings by first deriving the low dimensional dynamics of the system and examining the system bifurcations using a stability and steady-state analysis.

Asymmetry-induced isolated fully synchronized state in coupled oscillator populations.

A symmetry-breaking mechanism is investigated that creates bistability between fully and partially synchronized states in oscillator networks. Two populations of oscillators with unimodal frequency distribution and different amplitudes, in the presence of weak global coupling, are shown to simplify to a modular network with asymmetrical coupling. With increasing the coupling strength, a synchronization transition is observed with an isolated fully synchronized state. The results are interpreted theoretically in the thermodynamic limit and confirmed in experiments with chemical oscillators.

Coherence Stability and Effect of Random Natural Frequencies in Populations of Coupled Oscillators

We consider the (noisy) Kuramoto model, that is a population of \(N\) oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion. In the limit \(N \rightarrow \infty \) this model is accurately described by a (deterministic) Fokker–Planck equation. We study this equation and obtain quantitatively sharp results in the limit of weak disorder. We show that, in general, even when the natural frequencies have zero mean the oscillators synchronize (for sufficiently strong interaction) around a common rotating phase, whose frequency is sharply estimated. We also establish the stability properties of these solutions (in fact, limit cycles). These results are obtained by identifying the stable hyperbolic manifold of stationary solutions of an associated non disordered model and by exploiting the robustness of hyperbolic structures under suitable perturbations. When the disorder distribution is symmetric the speed vanishes and there is a one parameter family of stationary solutions, as pointed out by Sakaguchi (Prog Theor Phys 79:39–46, 1988): in this case we provide more precise stability estimates. The methods we use apply beyond the Kuramoto model and we develop here the case of active rotator models, that is the case in which the dynamics of each rotator in absence of interaction and noise is not simply a rotation.

The SCN is Comprised of a Population of Coupled Oscillators

The circadian clock in the suprachiasmatic nucleus (SCN) of the mammalian hypothalamus exhibits two necessary properties: (1) a mechanism for the generation of autonomous circadian rhythms in individual pacemaker cells, and (2) a means to synchronize the autonomous pacemaker cells. A variety of potential components of the endogenous pacemaker, including ion channels, second messengers, transcriptional factors, and the protein targets of kinases and transcription factors are reviewed. Similarly, reverse transmitter transport, extracellular ion fluxes, small membrane-diffusible molecules, glial regulation, and neural adhesion molecules are considered as possible synchronizing factors. Provisional criteria are suggested for empirical distinction of endogenous pacemaker versus synchronizing mechanisms.

Mutual Entrainment between Populations of Coupled Oscillators

Collective oscillations in a system of multiple populations of limit·cycle oscillators are studied. The oscillators are identical in each population, and besides their mutual coupling they are subject to noise. By means of a perturbation method, it is shown that a pair of populations with different collective frequencies is shown to exhibit synchronized/independent collective oscillations when the strength of their mutual coupling is sufficiently large/small. Furthermore, numerical simulations reveal a complicated bifurcation structure. We also study a system of four populations arranged in a ring. It is shown that the two populations which are coupled only indirectly can synchronize without entraining the intervening populations.

Mutual Entrainment between Populations of Coupled Oscillators

Mutual Entrainment between Populations of Coupled Oscillators

Origin of the Unique Feature of a Phase Transition in a Class of Large Populations of Coupled Oscillators

Origin of the Unique Feature of a Phase Transition in a Class of Large Populations of Coupled Oscillators