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Register a new userTransitions To the Long-Resident State in coupled chaotic oscillators
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The behaviors of coupled chaotic oscillators before complete synchronization were investigated. We report three phenomena: (1) The emergence of long-time residence of trajectories besides one of the saddle foci; (2) The tendency that orbits of the two oscillators get close becomes faster with increasing the coupling strength; (3) The diffusion of two oscillators phase difference is first enhanced and then suppressed. There are exact correspondences among these phenomena. The mechanism of these correspondences is explored. These phenomena uncover the route to synchronization of coupled chaotic oscillators.
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This paper presents a phase description of chaotic dynamics for the study of chaotic phase synchronization. A prominent feature of the proposed description is that it systematically incorporates the dynamics of the non-phase variables inherent in the system. Taking these non-phase dynamics into account is essential for capturing the complicated nature of chaotic phase synchronization, even in a qualitative manner. We numerically verified the validity of the proposed description for the R{o}ssler and Lorenz oscillators, and found that our method provides an accurate description of the characteristic distorted shapes of the synchronization regions of their chaotic oscillators. Furthermore, the proposed description allowed us to systematically explain the origin of this distortion.
Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual elements communicate is heterogeneous. Nevertheless, most of previous works considered the homogeneous case only. Here, we investigated the dynamical behaviors in a population of spatially distributed chaotic oscillators immersed in a heterogeneous environment. Various dynamical synchronization states such as oscillation death, phase synchronization, and complete synchronized oscillation as well as their transitions were found. More importantly, we uncovered a non-traditional quorum sensing transition: increasing the density would first lead to collective oscillation from oscillation quench, but further increasing the population density would lead to degeneration from complete synchronization to phase synchronization or even from phase synchronization to desynchronization. The underlying mechanism of this finding was attributed to the dual roles played by the population density. Further more, by treating the indirectly coupled systems effectively to the system with directly local coupling, we applied the master stability function approach to predict the occurrence of the complete synchronized oscillation, which were in agreement with the direct numerical simulations of the full system. The possible candidates of the experimental realization on our model was also discussed.
We investigate the diffusion coefficient of the time integral of the Kuramoto order parameter in globally coupled nonidentical phase oscillators. This coefficient represents the deviation of the time integral of the order parameter from its mean value on the sample average. In other words, this coefficient characterizes long-term fluctuations of the order parameter. For a system of N coupled oscillators, we introduce a statistical quantity D, which denotes the product of N and the diffusion coefficient. We study the scaling law of D with respect to the system size N. In other well-known models such as the Ising model, the scaling property of D is D sim O(1) for both coherent and incoherent regimes except for the transition point. In contrast, in the globally coupled phase oscillators, the scaling law of D is different for the coherent and incoherent regimes: D sim O(1/N^a) with a certain constant a>0 in the coherent regime and D sim O(1) in the incoherent regime. We demonstrate that these scaling laws hold for several representative coupling schemes.
We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analog of a classical Ising spin, networks of coupled parametric oscillators are considered as simulators of Ising spin models, aiming to efficiently calculate the ground state of an Ising network - a computationally hard problem. However, the coherent dynamics of coupled parametric oscillators can be considerably richer than that of Ising spins, depending on the nature of the coupling between them (energy preserving or dissipative), as was recently shown for two coupled parametric oscillators. In particular, when the energy-preserving coupling is dominant, the system displays everlasting coherent beats, transcending the Ising description. Here, we extend these findings to three coupled parametric oscillators, focusing in particular on the effect of frustration of the dissipative coupling. We theoretically analyze the dynamics using coupled nonlinear Mathieus equations, and corroborate our theoretical findings by a numerical simulation that closely mimics the dynamics of the system in an actual experiment. Our main finding is that frustration drastically modifies the dynamics. While in the absence of frustration the system is analogous to the two-oscillator case, frustration reverses the role of the coupling completely, and beats are found for small energy-preserving couplings.
Two symmetrically coupled populations of N oscillators with inertia $m$ display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendula. In particular, we report the first evidence of intermittent chaotic chimeras, where one population is synchronized and the other jumps erratically between laminar and turbulent phases. These states have finite life-times diverging as a power-law with N and m. Lyapunov analyses reveal chaotic properties in quantitative agreement with theoretical predictions for globally coupled dissipative systems.
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