Transitions to Long-Resident States in Coupled Chaotic Oscillators

The behaviour of coupled chaotic oscillators before complete synchronization is investigated. Long-time residence of trajectories appears besides one of the saddle foci. The tendency that orbits of the two oscillators get closer becomes faster with the increasing coupling strength. The diffusion of phase difference between the two oscillators 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.     

Synchronization of an ensemble of oscillators regulated by their spatial movement

Synchronization for a collection of oscillators residing in a finite two dimensional plane is explored. The coupling between any two oscillators in this array is unidirectional, viz., master-slave configuration. Initially the oscillators are distributed randomly in space and their autonomous time-periods follow a Gaussian distribution. The duty cycles of these oscillators, which work under an on-off scenario, are normally distributed as well. It is realized that random hopping of oscillators is a necessary condition for observing global synchronization in this ensemble of oscillators. Global synchronization in the context of the present work is defined as the state in which all the oscillators are rendered identical. Furthermore, there exists an optimal amplitude of random hopping for which the attainment of this global synchronization is the fastest. The present work is deemed to be of relevance to the synchronization phenomena exhibited by pulse coupled oscillators such as a collection of fireflies.     

Entangled chimeras in nonlocally coupled bicomponent phase oscillators: From synchronous to asynchronous chimeras

Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units, have been identified in various systems and generalized to coupled nonidentical oscillators. It has been shown that strong heterogeneity in the frequencies of nonidentical oscillators might be harmful to chimera states. In this work, we consider a ring of nonlocally coupled bicomponent phase oscillators in which two types of oscillators are randomly distributed along the ring: some oscillators with natural frequency ω₁ and others with ω₂ . In this model, the heterogeneity in frequency is measured by frequency mismatch |ω₁−ω₂| between the oscillators in these two subpopulations. We report that the nonlocally coupled bicomponent phase oscillators allow for chimera states no matter how large the frequency mismatch is. The bicomponent oscillators are composed of two chimera states, one supported by oscillators with natural frequency ω₁ and the other by oscillators with natural frequency ω₂. The two chimera states in two subpopulations are synchronized at weak frequency mismatch, in which the coherent oscillators in them share similar mean phase velocity, and are desynchronized at large frequency mismatch, in which the coherent oscillators in different subpopulations have distinct mean phase velocities. The synchronization–desynchronization transition between chimera states in these two subpopulations is observed with the increase in the frequency mismatch. The observed phenomena are theoretically analyzed by passing to the continuum limit and using the Ott-Antonsen approach.     

Zeno effect in quantum Newton's cradle

We describe a chain of quantum oscillators which behaves analogously to Newton's cradle. The energy swings between the ends of the chain with very low population in its interior. Moreover, the oscillators at the ends can entangle with each other with negligible entanglement with the intermediate oscillators that mediate the process. Up to a certain number of oscillators, the system evolves in a manner similar to two coupled oscillators. The conditions for such behavior and the characteristic periods are analyzed. When that number exceeds a threshold, the dynamical regime changes to virtually freezing. In the oscillatory regime, Zeno effect can be observed. The parallelism between the Zeno dynamics in quantum Newton's cradle and in two coupled oscillators is highlighted. Promising platforms to observe such phenomena in the laboratory are cavities in photonic-band-gap material and trapped ions.     

耦合相振子系统同步的序参量理论

节律行为,即系统行为呈现随时间的周期变化,在我们的周围随处可见.不同节律之间可以通过相互影响、相互作用产生自组织,其中同步是最典型、最直接的有序行为,它也是非线性波、斑图、集群行为等的物理内在机制.不同的节律可以用具有不同频率的振子(极限环)来刻画,它们之间的同步可以用耦合极限环系统的动力学来加以研究.微观动力学表明,随着耦合强度增强,振子同步伴随着动力学状态空间降维到一个低维子空间,该空间由序参量来描述.序参量的涌现及其所描述的宏观动力学行为可借助于协同学与流形理论等降维思想来进行.本文从统计物理学的角度讨论了耦合振子系统序参量涌现的几种降维方案,并对它们进行了对比分析.序参量理论可有效应用于耦合振子系统的同步自组织与相变现象的分析,通过进一步研究序参量的动力学及其分岔行为,可以对复杂系统的涌现动力学有更为深刻的理解.     

Synchronization of plant circadian oscillators with a phase delay effect of the vein network

Synchronization phenomena in coupled circadian oscillators of plant leaves were investigated experimentally using bioluminescence technology for a clock gene. Analyzing the phase of circadian oscillation, the phase-wave propagations and the phase delay caused by the vein network were observed. We describe these phase dynamics using a two-layer model with coupled Stuart-Landau equations. Global synchronization of circadian oscillators in the leaf is also investigated.     

Explosive synchronization through dynamical environment

We report the emergence of an explosive synchronization transition in the identical oscillators interacting indirectly through a network of dynamical agents. The transition from incoherent state to coherent state and vice–versa in these coupled oscillator exhibits an abrupt as well as irreversible. Such transition depends on the network topology as well as the interaction between the oscillators and dynamical agents rather than degree-frequency correlation in the network of oscillators. The occurrence of explosive synchronization is studied in details by using an appropriate order parameter for limit-cycle oscillators with respect to the different parameters like rewiring probability, average degree, and diffusion rate in dynamical agents.     

Strange Heat Flux in (An)Harmonic Networks

We study the heat transport in systems of coupled oscillators driven out of equilibrium by Gaussian heat baths. We illustrate with a few examples that such systems can exhibit “strange” transport phenomena. In particular, circulation of heat flux may appear in the steady state of a system of three oscillators only. This indicates that the direction of the heat fluxes can in general not be “guessed” from the temperatures of the heat baths. Although we primarily consider harmonic couplings between the oscillators, we explain why this strange behavior persists under weak anharmonic perturbations.     

Drift Intermittent Synchronization and Controllability in a Simple Model

A simple model of three coupled oscillators as an approximation of main modes behaviors in a spatial extended system is proposed. Multi-looping generalized synchronization and drift intermittent lag phase synchronization phenomena are found in this simple model. For a certain of parameters in which chaotic-like intermittent behavior exhibit the amplitudes and phases of three modes are controlled to be synchronized states via coupling them with an external periodic mode.     

Drift Intermittent Synchronization and Controllability in a Simple Model

A simple model of three coupled oscillators as an approximation of main modes behaviors in a spatial extended system is proposed. Multi-looping generalized synchronization and drift intermittent lag phase synchronization phenomena are found in this simple model. For a certain of parameters in which chaotic-like intermittent behavior exhibit the amplitudes and phases of three modes are controlled to be synchronized states via coupling them with an external periodic mode.     

Two scenarios of breaking chaotic phase synchronization

Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting oscillators, as in the case of classical synchronization of periodic oscillators. If interacting stochastic oscillators are weakly detuned, the phase coherency of the attractors persists when phase synchronization breaks. Conversely, if the control parameters differ considerably, the chaotic attractor becomes phase-incoherent under the conditions of phase synchronization break.     

1:1 Mode locking and generalized synchronization in mechanical oscillators

We describe the relation between the complete, phase and generalized synchronization of the mechanical oscillators (response system) driven by the chaotic signal generated by the driven system. We identified the close dependence between the changes in the spectrum of Lyapunov exponents and a transition to different types of synchronization. The strict connection between the complete synchronization (imperfect complete synchronization) of response oscillators and their phase or generalized synchronization with the driving system (the (1:1) mode locking) is shown. We argue that the observed phenomena are generic in the parameter space and preserved in the presence of a small parameter mismatch.     

Coupled catalytic oscillators: Beyond the mass-action law

We present Monte Carlo simulations of the reaction kinetics corresponding to two coupled catalytic oscillators in the case when oscillations result from the interplay between the reaction steps and adsorbate-induced surface restructuring. The model used is aimed to mimic oscillations on a single nm catalyst particle with two kinds of facets or on two catalyst particles on a support. Specifically, we treat the NO reduction by H(2) on a composite catalyst containing two catalytically active Pt(100) parts connected by an inactive link. The catalyst is represented by a rectangular fragment of a square lattice. The left- and right-hand parts of the lattice mimic Pt(100). With an appropriate choice of the model parameters, these sublattices play a role of catalytic oscillators. The central catalytically inactive sublattice is considered to be able only to adsorb NO reversibly and can be viewed as a Pt(111) facet or a support. The interplay of the reactions running on the catalytically active areas occurs via NO diffusion over the boundaries between the sublattices. Using this model, we show that the coupling of the catalytically active sublattices may synchronize nearly harmonic oscillations observed on these sublattices and also may result in the appearance of aperiodic partly synchronized oscillations. The spatio-temporal patterns corresponding to these regimes are nontrivial. In particular, the model predicts that, due to phase separation, the reaction may be accompanied by the formation of narrow NO-covered zones on the left and right sublattices near the boundaries between these sublattices and the central sublattice. Such patterns cannot be obtained by using the conventional mean-field reaction-diffusion equations based on the mass-action law. The experimental opportunities to observe the predicted phenomena are briefly discussed. (c) 2001 American Institute of Physics.     

On the occurrence of quasiperiodic motion on three tori

Two systems of three coupled non-linear oscillators are considered, one with linear and one with non-linear coupling. It is shown, with the help of numerical calculations of a number of indicators, that, in both cases, quasiperiodic flow can typically occur on three tori and survive under small changes in the parameters of the two systems. This result could be of consequence in our understanding of non-linear phenomena including turbulence.     

Mode locking in quantum optics

Mode locking phenomena in acoustics and in laser physics are discussed and are shown to share a feature of the forced oscillator: Oscillation takes place at the forcing frequency (or frequencies). The phenomena differ from simple forced oscillations in that they involve sustained oscillators (e.g., clocks, lasers) whose sustaining sources compete against the forcing signals in the choice of oscillation frequency. The locking phenomena are compared to second-order phase transitions in ferromagnetism and superconductivity where corresponding competition occurs between disordering thermal fluctuations and ordering correlations which reduce system energy.     

Diode Feedback Effects in Intense Relativistic Electron Beam Oscillators

The general operation of intense relativistic electron beam oscillators is described. These oscillators employ the well-known reflex triode phenomenon to plug the ends of a magnetically confined beam drift region by setting up efficient electron reflexing between the real cathode of an accelerator and a downstream virtual cathode. For a variety of magnetic traps and experimental conditions, it is shown that the inherent electron beam feedback from the drift region can be effectively utilized to reduce the electronion diode impedance and thereby permit good matching and energy transfer between the diode and a sub-ohm particle accelerator. A theoretical model is presented to interpret the observed phenomena.     

Disturbing synchronization: Propagation of perturbations in networks of coupled oscillators

We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the interaction network underlying the ensemble. The overall response of the system is resonant, exhibiting a maximum when the perturbation frequency coincides with the natural frequency of the phase oscillators. The individual response, on the other hand, can strongly depend on the distance to the place where the perturbation is applied. For small distances on a random network, the system behaves as a linear dissipative medium: the perturbation propagates at constant speed, while its amplitude decreases exponentially with the distance. For larger distances, the response saturates to an almost constant level. These different regimes can be analytically explained in terms of the length distribution of the paths that propagate the perturbation signal. We study the extension of these results to other interaction patterns, and show that essentially the same phenomena are observed in networks of chaotic oscillators.     

Multistability and chaotic beating of Duffing oscillators suspended on an elastic structure

We consider the dynamics of a number of externally excited chaotic oscillators suspended on an elastic structure. We show that for the given conditions of oscillations of the structure, initially uncorrelated chaotic oscillators become periodic and synchronous in clusters. In the periodic regime, we have observed multistability as two or four different attractors coexist in each cluster. A mismatch of the excitation frequency in the oscillators leads to the beating-like behaviour. We argue that the observed phenomena are generic in the parameter space and independent of the number of oscillators and their location on the elastic structure.     

耦合分数阶双稳态振子的同步、反同步与振幅死亡

研究了耦合分数阶振子的同步、反同步和振幅死亡等问题. 基于P-R振子在特定参数下的双稳态特性, 利用最大条件Lyapunov指数、最大Lyapunov指数和分岔图等数值方法分析发现, 通过选取初始条件和耦合强度, 可以控制耦合振子呈现混沌同步、混沌反同步、全部振幅死亡同步、全部振幅死亡反同步和部 分振幅死亡等丰富的动力学现象. 基于蒙特卡罗方法的原理, 在初始条件相空间中随机选取耦合振子的初始位置, 计算不同耦合强度下耦合振子的全部振幅死亡态、部分振幅死亡态和非振幅死亡态的比例, 从统计学角度表征了耦合分数阶双稳态振子的动力学特征. 几种有代表性的双稳态振子的吸引域进一步证明了统计方法的计算结果. 关键词： 振幅死亡 吸引域 双稳态     

Synchronization in arrays of coupled self-induced friction oscillators

We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to exponential model. Initially, a single degree of freedom mass-spring system on a moving belt is considered to check the type of motion of the system (periodic, non-periodic). Then the system is coupled in chain of identical oscillators starting from two, up to four oscillators. A reference probe of two coupled oscillators is applied in order to detect synchronization thresholds for both periodic and non-periodic motion of the system. The master stability function is applied to predict the synchronization thresholds for longer chains of oscillators basing on two oscillator probe. It is shown that synchronization is possible both for three and four coupled oscillators under certain circumstances. Our results confirmed that this technique can be also applied for the systems with discontinuities.