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Register a new userMobility induces global synchronization of oscillators in periodic extended systems
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We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which display local order. We use a statistical description valid for a large number of oscillators to show that for any finite system there is a critical spatial diffusion above which all wave-like solutions become unstable. Through Langevin simulations, we show that the transition to global synchronization is mediated by the relative size of attractor basins associated to wave-like states. Spatial diffusion disrupts these states and paves the way for the system to attain global synchronization.
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Driven by various kinds of noise, ensembles of limit cycle oscillators can synchronize. In this letter, we propose a general formulation of synchronization of the oscillator ensembles driven by common colored noise with an arbitrary power spectrum. To explore statistical properties of such colored noise-induced synchronization, we derive the stationary distribution of the phase difference between two oscillators in the ensemble. This analytical result theoretically predicts various synchronized and clustered states induced by colored noise and also clarifies that these phenomena have a different synchronization mechanism from the case of white noise.
Metabolic oscillations in single cells underlie the mechanisms behind cell synchronization and cell-cell communication. For example, glycolytic oscillations mediated by biochemical communication between cells may synchronize the pulsatile insulin secretion by pancreatic tissue, and a link between glycolytic synchronization anomalies and type-2 diabetes has been hypotesized. Cultures of yeast cells have provided an ideal model system to study synchronization and propagation waves of glycolytic oscillations in large populations. However, the mechanism by which synchronization occurs at individual cell-cell level and overcome local chemical concentrations and heterogenic biological clocks, is still an open question because of experimental limitations in sensitive and specific handling of single cells. Here, we show how the coupling of intercellular diffusion with the phase regulation of individual oscillating cells induce glycolytic synchronization waves. We directly measure the single-cell metabolic responses from yeast cells in a microfluidic environment and characterize a discretized cell-cell communication using graph theory. We corroborate our findings with simulations based on a kinetic detailed model for individual yeast cells. These findings can provide insight into the roles cellular synchronization play in biomedical applications, such as insulin secretion regulation at the cellular level.
We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks using the theory of semi-passive and passive systems. We show that the conductance-based neuronal models of Hodgkin-Huxley, Morris-Lecar, and the popular reduced models of FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a semi-passivity property, i.e. that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied (electrical) energy is bounded. As a result, for a wide range of coupling configurations, networks of these oscillators are guaranteed to possess ultimately bounded solutions. Moreover, we demonstrate that when the coupling is strong enough the oscillators become synchronized. Our theoretical conclusions are confirmed by computer simulations with coupled HR and ML oscillators. Finally we discuss possible instabilities in networks of oscillators induced by the diffusive coupling.
Carpets of actively bending cilia can exhibit self-organized metachronal coordination. Past research proposed synchronization by hydrodynamic coupling, but if such coupling is strong enough to overcome active phase noise had been addressed only for pairs of cilia. Using a multi-scale model calibrated by experimental cilia beat patterns, we find local multi-stability of wave modes. Yet, a single mode, corresponding to a dexioplectic wave, has predominant basin-of-attraction. Beyond a characteristic noise strength, we observe an abrupt loss of global synchronization even in finite systems.
A model of coupled molecular oscillators is proposed to study nonequilibrium thermodynamics of synchronization. We find that synchronization of nonequilibrium oscillators costs energy even when the oscillator-oscillator coupling is conservative. By solving the steady state of the many-body system analytically, we show that the system goes through a nonequilibrium phase transition driven by energy dissipation, and the critical energy dissipation depends on both the frequency and strength of the exchange reactions. Moreover, our study reveals the optimal design for achieving maximum synchronization with a fixed energy budget. We apply our general theory to the Kai system in Cyanobacteria circadian clock and predict a relationship between the KaiC ATPase activity and synchronization of the KaiC hexamers. The theoretical framework can be extended to study thermodynamics of collective behaviors in other extended nonequilibrium active systems.
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