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Register a new userOn the dynamics of traveling phase-oscillators with positive and negative couplings
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We investigate numerically the dynamics of traveling clusters in systems of phase oscillators, some of which possess positive couplings and others negative couplings. The phase distribution, speed of traveling, and average separation between clusters as well as order parameters for positive and negative oscillators are computed, as the ratio of the two coupling constants and/or the fraction of positive oscillators are varied. The traveling speed depending on these parameters is obtained and observed to fit well with the numerical data of the systems. With the help of this, we describe the conditions for the traveling state to appear in the systems with or without periodic driving.
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We investigate numerically the clustering behavior of a system of phase oscillators with positive and negative couplings under a periodic external driving field with a bimodal distribution of driving phases. The phase distribution and the mean speed of the traveling state, as well as the order parameter for synchronization, are computed as the driving amplitude is varied. We observe that the periodically-driven system can also host traveling states for parameters in the same range as those for the case of a system without a driving field. The traveling speed is found to depend non-monotonically on the driving amplitude. In particular, oscillators divide into four clusters and move in pairs. Further, depending on the driving amplitude, two kinds of traveling mode arise: pairs of clusters traveling in the same direction (symmetric mode) and in opposite directions (antisymmetric mode). In the latter case (antisymmetric traveling mode), the average phase speed of the whole system apparently vanishes. A phenomenological argument for such behavior is given.
We study the effects of Janus oscillators in a system of phase oscillators in which the coupling constants take both positive and negative values. Janus oscillators may also form a cluster when the other ones are ordered and we calculate numerically the traveling speed of three clusters emerging in the system and average separations between them as well as the order parameters for three groups of oscillators, as the coupling constants and the fractions of positive and Janus oscillators are varied. An expression explaining the dependence of the traveling speed on these parameters is obtained and observed to fit well the numerical data. With the help of this, we describe how Janus oscillators affect the traveling of the clusters in the system.
A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators we reduce the delay system to a non-delayed Langevin equation, which allows us to analytically compute the distribution of frequencies, and their corresponding residence times. The number of stable periodic orbits scales with the roundtrip delay time and coupling strength, but the noisy system visits only a fraction of the orbits, which scales with the square root of the delay time and is independent of the coupling strength. In contrast, the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators, and only weakly dependent on the coupling delay. Finally we investigate the effect of a detuning between the oscillators. We demonstrate the generality of our results with delay-coupled FitzHugh-Nagumo oscillators.
Different types of synchronization states are found when non-linear chemical oscillators are embedded into an active medium that interconnects the oscillators but also contributes to the system dynamics. Using different theoretical tools, we approach this problem in order to describe the transition between two such synchronized states. Bifurcation and continuation analysis provide a full description of the parameter space. Phase approximation modeling allows the calculation of the oscillator periods and the bifurcation point.
Recently, the explosive phase transitions, such as explosive percolation and explosive synchronization, have attracted extensive research interest. So far, most existing works investigate Kuramoto-type models, where only phase variables are involved. Here, we report the occurrence of explosive oscillation quenching in a system of coupled Stuart-Landau oscillators that incorporates both phase and amplitude dynamics. We observe three typical scenarios with distinct microscopic mechanism of occurrence, i.e., ordinary, hierarchical, and cluster explosive oscillation death, corresponding to different frequency distributions of oscillators, respectively. We carry out theoretical analyses and obtain the backward transition point, which is shown to be independent of the specific frequency distributions. Numerical results are consistent with the theoretical prediction.
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