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Synchronization among arrays of beating cilia is one of the emergent phenomena in biological processes at meso-scopic scales. Strong inter-ciliary couplings modify the natural beating frequencies, $\omega$, of individual cilia to produce a collective motion that moves around a group frequency $\omega_m$. Here we study the thermodynamic cost of synchronizing cilia arrays by mapping their dynamics onto a generic phase oscillator model. The model suggests that upon synchronization the mean heat dissipation rate is decomposed into two contributions, dissipation from each cilium's own natural driving force and dissipation arising from the interaction with other cilia, the latter of which can be interpreted as the one produced by a potential with a time-dependent protocol in the framework of our model. The spontaneous phase-synchronization of beating dynamics of cilia induced by strong inter-ciliary coupling is always accompanied with a significant reduction of dissipation for the cilia population, suggesting that organisms as a whole expend less energy by attaining a temporal order. At the level of individual cilia, however, a population of cilia with $|\omega|< \omega_m$ expend more amount of energy upon synchronization., Comment: 6 pages, 3 figures

Interacting dynamic agents can often exhibit synchronization. It has been reported that the rhythm all agents agree on in the synchronized state could be different from the average of intrinsic rhythms of individual agents. Hinted by such a real-world behavior of the interaction-driven change of the average phase velocity, we propose a modified version of the Kuramoto model, in which the ith oscillator of the phase ϕi interacts with other oscillator j only when the phase difference $${{\phi }}_{{j}}$$ϕj − $${{\phi }}_{i}$$ϕi is in a limited range [−βπ, απ]. From extensive numerical investigations, we conclude that the asymmetric dynamic interaction characterized by β ≠ α leads to the shift of the synchronized frequency with respect to the original distribution of the intrinsic frequency. We also perform and report our computer-based synchronization experiment, which exhibits the expected shift of the synchronized frequency of human participants. In analogy to interacting runners, our result roughly suggests that agents tend to run faster if they are more influenced by runners ahead than behind. We verify the observation by using a simple model of interacting runners.

We study the steady-state patterns of population of the coupled oscillators that sync and swarm, where the interaction distances among oscillators have finite-cutoff in interaction distance. We examine how the static patterns known in the infinite-cutoff are reproduced or deformed, and explore a new static pattern that does not appear until a finite-cutoff is considered. All steady-state patterns of the infinite-cutoff, static sync, static async, and static phase wave are respectively repeated in space for proper finite-cutoff ranges. Their deformation in shape and density takes place for the other finite-cutoff ranges. Bar-like phase wave states are observed, which has not been the case for the infinite-cutoff. All the patterns are investigated via numerical and theoretical analysis., 9 pages, 8 figures

We have frequently encountered the rapid changes that prevalent opinion of the social community is toppled by a new and opposite opinion against the pre-exiting one. To understand this interesting process, mean-field model with infinite-interaction range has been mostly considered in previous studies S. A. Marvel et al., Phys. Rev. Lett. 110, 118702(2012). However, the mean-field interaction range is lack of reality in the sense that any individual cannot interact with all of the others in the community. Based on it, in the present work, we consider a simple model of opinion consensus so-called basic model on the low-dimensional lattices ($d$=1,2) with finite interaction range. The model consists of four types of subpopulations with different opinions: $A, B, AB$, and the zealot of $A$ denoted by $A_c$, following the basic model shown in the work by S. A. Marvel et al.. Comparing with their work, we consider the finite range of the interaction, and particularly reconstruct the lattice structure by adding new links when the two individuals have the distance $

Twisted states with nonzero winding numbers composed of sinusoidally coupled identical oscillators have been observed in a ring. The phase of each oscillator in these states constantly shifts, following its preceding neighbor in a clockwise direction, and the summation of such phase shifts around the ring over $2\ensuremath{\pi}$ characterizes the winding number of each state. In this work, we consider finite-sized $d$-dimensional hypercubic lattices, namely, square ($d=2$) and cubic ($d=3$) lattices with periodic boundary conditions. For identical oscillators, we observe new states in which the oscillators belonging to each line (plane) for $d=2$ ($d=3$) are phase synchronized with nonzero winding numbers along the perpendicular direction. These states can be reduced into twisted states in a ring with the same winding number if we regard each subset of phase-synchronized oscillators as one single oscillator. For nonidentical oscillators with heterogeneous natural frequencies, we observe similar patterns with slightly heterogeneous phases in each line $(d=2)$ and plane $(d=3)$. We show that these states generally appear for random configurations when the global coupling strength is larger than the critical values for the states.

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Here we explore systems in which both synchronization and swarming occur together. Specifically, we consider oscillators whose phase dynamics and spatial dynamics are coupled. We call them swarmalators, to highlight their dual character. A case study of a generalized Kuramoto model predicts five collective states as possible long-term modes of organization. These states may be observable in groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact., Collective self-organized behavior can be observed in a variety of systems such as colloids and microswimmers. Here O’Keeffe et al. propose a model of oscillators which move in space and tend to synchronize with neighboring oscillators and outline five types of collective self-organized states.

We consider a mean-field model of coupled phase oscillators with random heterogeneity in the coupling strength. The system that we investigate here is a minimal model that contains randomness in diverse values of the coupling strength, and it is found to return to the original Kuramoto model [Y. Kuramoto, Prog. Theor. Phys. Suppl. 79, 223 (1984)10.1143/PTPS.79.223] when the coupling heterogeneity disappears. According to one recent paper [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015)10.1103/PhysRevE.92.022122], when the natural frequency of the oscillator in the system is "deterministically" chosen, with no randomness in it, the system is found to exhibit the finite-size scaling exponent ν[over ¯]=5/4. Also, the critical exponent for the dynamic fluctuation of the order parameter is found to be given by γ=1/4, which is different from the critical exponents for the Kuramoto model with the natural frequencies randomly chosen. Originally, the unusual finite-size scaling behavior of the Kuramoto model was reported by Hong et al. [H. Hong, H. Chaté, H. Park, and L.-H. Tang, Phys. Rev. Lett. 99, 184101 (2007)10.1103/PhysRevLett.99.184101], where the scaling behavior is found to be characterized by the unusual exponent ν[over ¯]=5/2. On the other hand, if the randomness in the natural frequency is removed, it is found that the finite-size scaling behavior is characterized by a different exponent, ν[over ¯]=5/4 [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015)10.1103/PhysRevE.92.022122]. Those findings brought about our curiosity and led us to explore the effects of the randomness on the finite-size scaling behavior. In this paper, we pay particular attention to investigating the finite-size scaling and dynamic fluctuation when the randomness in the coupling strength is considered.

We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction $p$ of oscillators are positively coupled, attracting all others, while the remaining fraction $1-p$ are negatively coupled, repelling all others. The frequencies and couplings are deterministically chosen in a manner which correlates them, thereby correlating the two types of disorder in the model. We first explore the effect of this correlation on the system's phase coherence. We find that there is a a critical width $\gamma_c$ in the frequency distribution below which the system spontaneously synchronizes. Moreover, this $\gamma_c$ is independent of $p$. Hence, our model and the traditional Kuramoto model (recovered when $p=1$) have the same critical width $\gamma_c$. We next explore the critical behavior of the system by examining the finite-size scaling and the dynamic fluctuation of the traditional order parameter. We find that the model belongs to the same universality class as the Kuramoto model with deterministically (not randomly) chosen natural frequencies for the case of $p, Comment: 7 pages, 6 figures

We consider a system of coupled swarmalators moving in two dimensional space and explore its collective behavior. Here the swarmalators represent the oscillators that can sync and swarm in space, following the previous study [O’Keeffe et al., Nat. Commun., 8, 1504 (2017)]. The internal state of each swarmalator is represented by its phase angle, and the swarmalators are free to move in the plane according to an equation of motion where the phase and spatial dynamics are coupled with each other. In particular, the phase coupling between the swarmalators is attractive (positive) one, so the coupling makes the swarmalators have their phase difference minimized. The collective behavior of the system is found to be different depending on the extent of the interplay between the phase and spatial dynamics: Specifically, when the extent of the interplay between the phase and spatial dynamics is so weak as to be negligible, the phase dynamics of our system recovers that of the conventional mean-field X Y model. On the other hand, when a certain extent of the interplay is present, the system is found to exhibit the correlated phase where the overall order does not occur. Interestingly, it is found that the correlated phase is the same as the active phase wave found in the system of swarmalators with repulsive phase coupling [O’Keeffe et al., Nat. Commun., 8, 1504 (2017)]. We also find that the system exhibits two different phase transitions: One is the transition from the sync state to the active phase wave state, and the other one is the transition from the active phase wave state to the async state. We perform the finite-size scaling analysis and investigate the transition nature.We consider a system of coupled swarmalators moving in two dimensional space and explore its collective behavior. Here the swarmalators represent the oscillators that can sync and swarm in space, following the previous study [O’Keeffe et al., Nat. Commun., 8, 1504 (2017)]. The internal state of each swarmalator is represented by its phase angle, and the swarmalators are free to move in the plane according to an equation of motion where the phase and spatial dynamics are coupled with each other. In particular, the phase coupling between the swarmalators is attractive (positive) one, so the coupling makes the swarmalators have their phase difference minimized. The collective behavior of the system is found to be different depending on the extent of the interplay between the phase and spatial dynamics: Specifically, when the extent of the interplay between the phase and spatial dynamics is so weak as to be negligible, the phase dynamics of our system recovers that of the conventional mean-field X Y model. ...

We consider a mean-field model of coupled phase oscillators with quenched disorder in the coupling strengths and natural frequencies. When these two kinds of disorder are uncorrelated (and when the positive and negative couplings are equal in number and strength), it is known that phase coherence cannot occur and synchronization is absent. Here we explore the effects of correlating the disorder. Specifically, we assume that any given oscillator either attracts or repels all the others, and that the sign of the interaction is deterministically correlated with the given oscillator's natural frequency. For symmetrically correlated disorder with zero mean, we find that the system spontaneously synchronizes, once the width of the frequency distribution falls below a critical value. For asymmetrically correlated disorder, the model displays coherent traveling waves: the complex order parameter becomes nonzero and rotates with constant frequency different from the system's mean natural frequency. Thus, in both cases, correlated disorder can trigger phase coherence., 6 pages, 6 figures

Some of the most pivotal moments in intellectual history occur when a new ideology sweeps through a society, supplanting an established system of beliefs in a rapid revolution of thought. Yet in many cases the new ideology is as extreme as the old. Why is it then that moderate positions so rarely prevail? Here, in the context of a simple model of opinion spreading, we test seven plausible strategies for deradicalizing a society and find that only one of them significantly expands the moderate subpopulation without risking its extinction in the process., Comment: 9 pages, 5 figures

We consider a variant of the Kuramoto model, in which all the oscillators are now assumed to have the same natural frequency, but some of them are negatively coupled to the mean field. These "contrarian" oscillators tend to align in antiphase with the mean field, whereas the positively coupled "conformist" oscillators favor an in-phase relationship. The interplay between these effects can lead to rich dynamics. In addition to a splitting of the population into two diametrically opposed factions, the system can also display traveling waves, complete incoherence, and a blurred version of the two-faction state. Exact solutions for these states and their bifurcations are obtained by means of the Watanabe-Strogatz transformation and the Ott-Antonsen ansatz. Curiously, this system of oscillators with identical frequencies turns out to exhibit more complicated dynamics than its counterpart with heterogeneous natural frequencies., Comment: 7 pages, 4 figures, to appear in Phys. Rev. E

We study synchronization and noise-induced resonance phenomena in systems of globally coupled oscillators, each possessing finite inertia. The behavior of the order parameter, which measures collective synchronization of the system, is investigated as the noise level and the coupling strength are varied, and hysteretic behavior is manifested. The power spectrum of the phase velocity is also examined and the quality factor as well as the response function is obtained to reveal noise-induced resonance behavior., to be published in Phys. Rev. E