Intermittent lag synchronization in a driven system of coupled oscillators

We study intermittent lag synchronization in a system of two identical mutually coupled Duffing oscillators with parametric modulation in one of them. This phenomenon in a periodically forced system can be seen as intermittent jump from phase to lag synchronization, during which the chaotic trajectory visits a periodic orbit closely. We demonstrate different types of intermittent lag synchronizations, that occur in the vicinity of saddle-node bifurcations where the system changes its dynamical state, and characterize the simplest case of period-one intermittent lag synchronization.     

Synchronization of self-sustained oscillators inertially coupled through common damped system

We study the dynamics of two self-oscillating systems inertially coupled to a linear oscillator. This interaction mechanism results in various types of synchronous motions such as in-phase, anti-phase and phase synchronization. We demonstrate the existence of mono-stable regimes and multi-stable behavior with two or more coexisting attractors. We present the bifurcational analysis revealing transition mechanisms between these regimes. In the multi-stable case, we examine the role of coupling parameter and shape of oscillations (the parameter indicating nonlinearity and strength of the damping) in various structure formations of attraction basins.     

谐和与噪声联合作用下Duffing振子的安全盆分叉与混沌

研究了软弹簧Duffing振子在确定性谐和外力和有界随机噪声联合作用下，系统安全盆的侵蚀和混沌现象.推导出系统的随机Melnikov过程，根据Melnikov过程在均方意义上出现简单零点的条件给出了系统出现混沌的临界值，然后用数值模拟方法计算了系统的安全盆分叉点.结果表明，由于随机扰动的影响，系统的安全盆分叉点发生了偏移，并且使得混沌容易发生. 关键词： Duffing振子 安全盆 分叉 混沌     

Synchronization of coupled stochastic oscillators: The effect of topology

We study sets of genetic networks having stochastic oscillatory dynamics. Depending on the coupling topology we find regimes of phase synchronization of the dynamical variables. We consider the effect of time-delay in the interaction and show that for suitable choices of delay parameter, either in-phase or anti-phase synchronization can occur.      

Extraction of periodic signals in chaotic secure communication using Duffing oscillators

This paper presents a novel approach to extract the periodic signals masked by a chaotic carrier. It verifies that the driven Duffing oscillator is immune to the chaotic carrier and sensitive to certain periodic signals. A preliminary detection scenario illustrates that the frequency and amplitude of the hidden sine wave signal can be extracted from the chaotic carrier by numerical simulation. The obtained results indicate that the hidden messages in chaotic secure communication can be eavesdropped utilizing Duffing oscillators.     

Experimental investigation of the response of a harmonically excited hard Duffing oscillator

A single degree-of-freedom torsional vibratory system, which constitutes a third-order dissipative dynamical system, has been fabricated as a mechanical analogue of hard Duffing equation with strong nonlinearity. The forced response of the system reveals complicated and chaotic motion at low frequency regime. Besides usual jump phenomenon, unpredictable jump phenomenon with two and three coexisting periodic attractors is also observed.      

脉冲激励下环形耦合Duffing振子间的瞬态同步突变现象

研究非周期信号激励下Duffing振子动力学行为变化特征时,发现处于倍周期分岔的环形耦合Duffing振子系统,在一定的参数条件下,脉冲信号能引起其中一个振子与其他振子运动轨迹间出现短暂失同步的现象即瞬态同步突变现象.利用这种现象可以快速检测出强噪声背景中的微弱脉冲信号,从而扩展了现有的Duffing振子对非周期信号的检测范围及应用领域. 关键词： 瞬态同步突变 微弱信号检测 脉冲信号 Duffing振子     

基于耦合Duffing振子的局部放电信号检测方法研究

以双向环形耦合Duffing振子系统为对象, 研究脉冲信号激励下耦合振子间动力学行为变化特征时, 发现其与单向环形耦合Duffing振子系统类似, 在一定的参数条件下, 脉冲信号能引起其中一个振子与其他振子运动轨迹间出现短暂失同步的现象即瞬态同步突变现象. 基于这种现象, 提出了一种微弱脉冲信号检测的新方法, 用于检测强噪声背景中的局部放电脉冲信号. 实验测试表明, 利用本文方法对不同放电电极的局部放电脉冲信号进行检测时, 在低信噪比条件下可取得良好的检测效果, 进而扩展了现有的Duffing振子对非周期信号的检测范围及应用领域. 关键词： 耦合Duffing 振子 微弱信号检测 瞬态同步突变 局部放电脉冲信号     

Synchronization of mutually coupled systems

General operation conditions to obtain anticipated or retarded synchronization in a mutually coupled system with feedback are analyzed. Different from a unidirectionally coupled system, which type of synchronization will occur in a mutually coupled system does not solely depend on the difference between the feedback-delay time and the coupling-delay time. We find that in addition to the feedback/coupling delay times, feedback strengths and coupling strengths all determine whether the system will preform anticipated or retarded synchronization. Experimental implementation using semiconductor lasers subject to optoelectronic feedback is provided as an example. A set of experimental data is presented and discussed.     

Synchronization in a multiplex network of gene oscillators

Study of the synchronization in the network of gene oscillator network has vital importance in understanding of rhythmicity of molecular and cellular activities. In this paper, we analyze a network of linearly coupled genetic oscillators in a multiplex structure. The coupling strength values are changed and the coupling range is considered to be fixed, but different in the two layers. The analyses are done in two cases of periodic and chaotic oscillations. By computing the statistical measures, the interlayer and intralayer synchronization states are studied. The results show that the layer with higher coupling range has more enhanced synchrony and is less affected by the turbulent behavior of the other layer. On the other hand, the layer with lower coupling range approaches synchronization by strengthening the interlayer and intralayer couplings. The interlayer synchronization is also achieved in high coupling strength values.     

Chaos and localization in coupled quartic oscillators

We discuss some of the models for eigenfunction localization in Hamiltonian systems. In particular, we review some of our work on classical parametric scaling of orbits and identification of localized states in a two-dimensional quartic oscillator system which is deep in the classically chaotic region. We show that visual methods are a necessary complement to quantitative methods based on information entropies. Our preliminary results indicate that the periodic orbit stability determines the degree of localization in a class of states, even when the stable regions are of negligible measure.     

Duffing振子微弱信号检测方法研究

在前期实验工作的基础上,从理论分析的角度,提出了利用Duffing振子从大周期态向混沌态的相变 作为判据的微弱周期信号检测方法,给出了检测原理,并论证了其可行性;从过渡带影响和检测概率两方面 将该方法与传统的检测方法进行了比较分析,并对两者的检测性能进行了仿真对比.分析和仿真结果都显示,相同条件下, Duffing振子从大周期态向混沌态的相变受过渡带影响更小,所提方法具有更好的检测性能. 实验数据还表明, Duffing振子检测微弱信号只能基于单向相变, 利用阵发混沌进行频差检测只适用于待测信号信噪比较高的情况. 关键词： Duffing 混沌 检测 过渡带     

用两耦合非线性振子模型研究量子纠缠和相干性

我们研究两耦合非线性振子模型的量子纠缠和量子相干动力学, 结果表明在适当条件下, 纠缠熵与相干度是正相关的. 我们也讨论纠缠熵和相干度与两振子子相互作用能的联系.     

用两耦合非线性振子模型研究量子纠缠和相干性

我们研究两耦合非线性振子模型的量子纠缠和量子相干动力学,结果表明在适当条件下,纠缠熵与相干度是正相关的.我们也讨论纠缠熵和相干度与两振子相互作用能的联系.     

Synchronization in an array of coupled Boolean networks

This Letter presents an analytical study of synchronization in an array of coupled deterministic Boolean networks. A necessary and sufficient criterion for synchronization is established based on algebraic representations of logical dynamics in terms of the semi-tensor product of matrices. Some basic properties of a synchronized array of Boolean networks are then derived for the existence of transient states and the upper bound of the number of fixed points. Particularly, an interesting consequence indicates that a “large” mismatch between two coupled Boolean networks in the array may result in loss of synchrony in the entire system. Examples, including the Boolean model of coupled oscillations in the cell cycle, are given to illustrate the present results.     

超混沌振荡器的混沌耦合同步

提出了两种应用单变量单向混沌耦合同步超混沌振荡器的同步方案。首先给出了混沌耦合同步方案的数学证明，然后通过数值仿真证实了该混沌耦合同步方案的正确性和有效性。最后通过计算条件李雅谱诺夫指数，比较了不同耦合强度下，两种混沌耦合同步和典型的连续耦合同步的同步性能。计算表明在一定的耦合强度下，混沌耦合比典型的连续耦合同步速度快。     

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.     

Frequency analysis with coupled nonlinear oscillators

We present a method to obtain the frequency spectrum of a signal with a nonlinear dynamical system. The dynamical system is composed of a pool of adaptive frequency oscillators with negative mean-field coupling. For the frequency analysis, the synchronization and adaptation properties of the component oscillators are exploited. The frequency spectrum of the signal is reflected in the statistics of the intrinsic frequencies of the oscillators. The frequency analysis is completely embedded in the dynamics of the system. Thus, no pre-processing or additional parameters, such as time windows, are needed. Representative results of the numerical integration of the system are presented. It is shown, that the oscillators tune to the correct frequencies for both discrete and continuous spectra. Due to its dynamic nature the system is also capable to track non-stationary spectra. Further, we show that the system can be modeled in a probabilistic manner by means of a nonlinear Fokker-Planck equation. The probabilistic treatment is in good agreement with the numerical results, and provides a useful tool to understand the underlying mechanisms leading to convergence.     

Synchronization of oscillators coupled through an environment

We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate synchronization of systems of oscillators which are weakly coupled, in the sense that the influence of the oscillators on the environment is weak. We prove that arbitrarily weak coupling will synchronize the oscillators, provided that this coupling is of the ‘right’ sign. We illustrate our general results by applications to a model of coupled GnRH neuron oscillators proposed by Khadra and Li [A. Khadra, Y.X. Li, A model for the pulsatile secretion of gonadotropin-releasing hormone from synchronized hypothalamic neurons, Biophys. J. 91 (2006) 74-83.], and to indirectly weakly-coupled λ-ω oscillators.     

Synchronization of coupled oscillators on small-world networks

We investigate the synchronous dynamics of Kuramoto oscillators and van der Pol oscillators on Watts-Strogatz type small-world networks. The order parameters to characterize macroscopic synchronization are calculated by numerical integration. We focus on the difference between frequency synchronization and phase synchronization. In both oscillator systems, the critical coupling strength of the phase order is larger than that of the frequency order for the small-world networks. The critical coupling strength for the phase and frequency synchronization diverges as the network structure approaches the regular one. For the Kuramoto oscillators, the behavior can be described by a power-law function and the exponents are obtained for the two synchronizations. The separation of the critical point between the phase and frequency synchronizations is found only for small-world networks in the theoretical models studied.