Synchronization of homoclinic chaos

Homoclinic chaos is characterized by regular geometric orbits occurring at erratic times. Phase synchronization at the average repetition frequency is achieved by a tiny periodic modulation of a control parameter. An experiment has been carried on a CO(2) laser with feedback, set in a parameter range where homoclinic chaos occurs. Any offset of the modulation frequency from the average induces phase slips over long times. Perfect phase synchronization is recovered by slow changes of the modulation frequency based upon the sign and amplitude of the slip rate. Satellite synchronization regimes are also realized, with variable numbers of homoclinic spikes per period of the modulation.     

Experimental characterization of the transition to phase synchronization of chaotic CO2 laser systems

We investigate the transition route to phase synchronization in a chaotic laser with external modulation. Such a transition is characterized by the presence of a regime of periodic phase synchronization, in which phase slips occur with maximal coherence in the phase difference between output signal and external modulation. We provide the first experimental evidence of such a regime and demonstrate that it occurs at the crossover point between two different scaling laws of the intermittent-type behavior of phase slips.     

Controlling hyperchaos and synchronizing periodic states in the DOPO

It has been found out that hyperchaotic behaviors can be controlled to enter periodicity state by modulating the detuned parameters in degenerated optical parameter oscillator (DOPO) with different periodic orbits from different modulation index at the same modulation frequency, or from different modulation frequency at the same modulation index. It was shown that the periodic orbits of the DOPOs modulated through sinusoid can be resulted in identical synchronization or inversed synchronization only in the case that the largest Lyapunov exponent exponent of the system is negative.PACS: 42.65.Sf     

注入半导体激光器混沌相位周期控制方法研究

提出外部光注入半导体激光器混沌相位控制方法，通过周期调制注入光的相位相移将激光器的混沌控制到多种周期状态.数值结果表明：在不同强度光注入下，(1)通过半波长周期相位相移调制控制混沌激光到周期态、双周期态、三周期态、四周期态以及多周期态等；(2)通过四分之一波长周期相位相移调制控制混沌激光到周期态和多周期态，并在高频调制控制时能够产生激光锁模现象，其锁模区域是19—21GHz；(3)波长周期相位相移调制控制也能使混沌激光控制到三周期态和多周期态等. 关键词： 混沌 控制 激光器 周期     

噪声在外加周期信号控制强湍中的作用研究

研究了噪声在控制中的作用.研究发现,较小强度的偏噪声信号能够使系统失去层流态,重新进入无序态,此时模式之间的广义相同步也失去了;而噪声强度较大时,系统则能够维持准周期的层流态,模式相位之间依然能够达到广义相同步. 关键词： 相同步 时空混沌 湍流 非线性漂移波     

直接相位调制产生周期性线性啁啾脉冲特性研究

提出一种利用周期性抛物线调制信号对光脉冲进行相位调制以获得周期性线性啁啾脉冲的方法, 并对其进行了数值模拟与实验研究. 数值模拟结果表明: 增益饱和效应、群速度色散以及同步误差对啁啾脉冲的时间-光谱特性影响较大; 自相位调制对啁啾脉冲的影响较小. 实验获得了0.52 nm带宽的周期性线性啁啾脉冲, 与模拟结果符合较好. 实验结果同时表明装置中存在较大的偏振模色散, 导致幅频效应较大, 后续的研究中需加入对此的考虑. 模拟及实验研究表明: 直接相位调制是一种新型的可方便地获得周期性线性啁啾脉冲的方法, 其在光谱色散平滑中具有潜在应用. 关键词： 直接相位调制 周期性线性啁啾脉冲 幅频效应     

Phase synchronization in tilted deterministic ratchets

We study phase synchronization for a ratchet system. We consider the deterministic dynamics of a particle in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues, which represent regions of synchronization in parameter space, and discuss their implications for transport in ratchets.     

Phase synchronization in a two-mode solid state laser: Periodic modulations with the second relaxation oscillation frequency of the laser output

Phase synchronization (PS) in a periodically pump-modulated two-mode solid state laser is investigated. Although PS in the laser system has been demonstrated in response to a periodic modulation with the main relaxation oscillation (RO) frequency of the free-running laser, little is known about the case of modulation with minor RO frequencies. In this Letter, the empirical mode decomposition (EMD) method is utilized to decompose the laser time series into a set of orthogonal modes and to examine the intrinsic PS near the frequency of the second RO. The degree of PS is quantified by means of a histogram of phase differences and the analysis of Shannon entropy.     

Experimental observation of chaotic phase synchronization of a periodically pump-modulated multimode microchip Nd:YVO4 laser

In this Letter we demonstrate the experimental observation of chaotic phase synchronization (CPS) in a periodically pump-modulated multimode microchip Nd:YVO₄ laser. PS transition is displayed via the stroboscopic technique. We apply the recurrence probability and correlation probability of recurrence to estimate the degree of PS. The degree of PS is studied taking into account the modulation amplitude and modulation frequency. We also propose an experimental compatible numerical simulation to reflect the fact that the Arnold tongues are experimentally and numerically exhibited in the periodically pump-modulated multimode microchip Nd:YVO₄ laser.     

Synchronization, multistability and basin crisis in coupled pendula

The synchronization dynamics of two linearly coupled pendula is studied in this paper. Based on the Lyapunov stability theory and Linear matrix inequality (LMI); some necessary and sufficient conditions for global asymptotic synchronization are derived from which an estimated threshold coupling k_th, for the on-set of full synchronization is obtained. The numerical value of k_th determined from the average energies of the systems is in good agreement with theoretical analysis. Prior to the on-set of synchronization, the boundary crisis of the chaotic attractor is identified. In the bistable states, where two asymmetric periodic attractors co-exist, it is shown that the coupled pendula can attain multistable states via a new dynamical transition—the basin crisis that occur prior to the on-set of stable synchronization. The essential feature of basin crisis is that the two co-existing attractors are destroyed while new three or more co-existing attractors of the same or different periodicity are created. In addition, the linear perturbation technique and the Routh-Hurwitz criteria are employed to investigate the stability of steady states, and clearly identify the different types of bifurcations likely to be encountered. Finally, two-parameter phase plots, show various regions of chaos, hyperchaos and periodicity.     

Intermittent lag synchronization in a nonautonomous system of coupled oscillators

Synchronization properties of two identical mutually coupled Duffing oscillators with parametric modulation in one of them are studied. Intermittent lag synchronization is observed in the vicinity of saddle-node bifurcations where the system changes its dynamical state. This phenomenon is seen as intermittent jumps from phase to lag synchronization, during which the chaotic trajectory visits closely a periodic orbit. Different types of intermittent lag synchronization are demonstrated and the simplest case of period-one lag synchronization is analyzed.     

Beam breakup and modulational instability in a bulk type I quadratic medium

The effect of a small modulation superimposed on a strip (1D) solitary wave propagating in a bulk quadratic medium was investigated both analytically and numerically near Type I phase matching. General, exact results were obtained. By using first order perturbation theory, we obtained the gain coefficient for the modulational instability and the modulation cut-off frequency and we investigated their dependence on various beam and material parameters. The wave evolves into a clean periodic sequence of solitary waves and does not reproduce the incident beam. We showed that the beam breakup observed experimentally is due entirely to noise induced modulational instability.     

光纤中扰动的小信号增益

从非线性薛定谔方程出发,在小信号近似下,推导并求解了光纤中扰动相位和幅度的演化方程,利用得到的扰动相位及功率增益的表达式,研究了初相位和频率对传输过程中扰动增益的影响。研究表明：扰动的初相位对扰动增益的初值和初始阶段的演化规律有重要影响;取决于扰动初相位,任何一个频率的扰动增益都有可能达到一个共同的最大值;在被认为无调制不稳定的正色散区和扰动频率大于截止频率的负色散区,扰动增益随距离是振荡的;在被认为有调制不稳定的扰动频率小于截止频率的负色散区,频率相同而初相位不同的扰动增益将经历不同形式的演化后趋于同一正值。     

Dynamical tracking of unstable periodic orbits

Tracking unstable periodic orbits and its stabilization by large periodic modulation of a control parameter are studied numerically in the Hénon map and laser equations. Some important scaling relations linking the tracking range to the modulation amplitude and frequency are deduced. The results obtained with both models are compared. Experimental realization of dynamical tracking is demonstrated in a loss-driven CO₂ laser where cavity detuning or losses are periodically modulated.     

A geometric theory of chaotic phase synchronization

A rigorous mathematical treatment of chaotic phase synchronization is still lacking, although it has been observed in many numerical and experimental studies. In this article we address the extension of results on phase synchronization in periodic oscillators to systems with phase coherent chaotic attractors with small phase diffusion. As models of such systems we consider special flows over diffeomorphisms in which the neutral direction is periodically perturbed. A generalization of the Averaging Theorem for periodic systems is used to extend Kuramoto's geometric theory of phase locking in periodically forced limit cycle oscillators to this class of systems. This approach results in reduced equations describing the dynamics of the phase difference between drive and response systems over long time intervals. The reduced equations are used to illustrate how the structure of a chaotic attractor is important in its response to a periodic perturbation, and to conclude that chaotic phase coherent systems may not always be treated as noisy periodic oscillators in this context. Although this approach is strictly justified for periodic perturbations affecting only the phase variable of a chaotic oscillator, we argue that these ideas are applicable much more generally.     

Integrated ferroelectric millimeter-wave phase shifters with a periodic structure

Integrated phase shifters with a periodic structure that includes BaSrTiO₃ ferroelectric varactors parallel-and series-connected to the transmission line are investigated theoretically and experimentally. The phase shifters are designed for the frequency range 26–32 GHz. The dispersion characteristics and insertion losses in the transmission line of the phase shifters are analyzed with regard to the dependence of the capacitance and loss tangent of the varactors on control voltage and temperature. It is shown that parasitic amplitude modulation in the phase shifters can be suppressed if the connection scheme of the varactors takes into account the voltage dependence of the their loss tangent. In the phase shifters with series-connected varactors, the temperature dependence of the phase shift is much weaker than in those with parallel-connected varactors.     

Chaotic phase synchronization in small-world networks of bursting neurons

We investigate the chaotic phase synchronization in a system of coupled bursting neurons in small-world networks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that phase synchronization is largely facilitated by a large fraction of shortcuts, but saturates when it exceeds a critical value. We also study the external chaotic phase synchronization of bursting oscillators in the small-world network by a periodic driving signal applied to a single neuron. It is demonstrated that there exists an optimal small-world topology, resulting in the largest peak value of frequency locking interval in the parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this interval increases with the driving amplitude, but decrease rapidly with the network size. We infer that the externally applied driving parameters outside the frequency locking region can effectively suppress pathologically synchronized rhythms of bursting neurons in the brain.     

用自适应脉冲微扰引导混沌系统到周期解

用自适应脉冲微扰方法控制的系统的某个系统变量作为驱动,设计了一种自适应控制器方法对两个或多个响应混沌系统进行脉冲微扰,引导这些系统从混沌运动到低周期运动,实现同时控制多个混沌系统到不同的周期态. 当选择相同的自适应控制器输入变量实施脉冲微扰时,还可控制两个或多个混沌系统达到不同的周期态同步. 通过对R?ssler混沌系统的仿真研究证实了方法的有效性. 关键词： 混沌控制 系统参量 自适应控制器 脉冲微扰 周期态同步     

Compression of whistler waves in a plasma with a nonstationary magnetic field

We present the results of our experiments in which the propagation of whistler waves in a plasma with a nonstationary magnetic-field perturbation (B=B₀+δB(t), δB/B₀ ≤ 5%) was investigated. The parametric and dispersive phenomena in a variable magnetic field were studied on the unique Krot plasma bench (the plasma column was 4 m in length and 1.5 m in diameter). A periodic field perturbation is shown to lead to an amplitude-frequency modulation of the whistler wave and to fragmentation of the signal into separate frequency-modulated wavepackets followed by their compression. The formation and compression of pulses is attributable to strong whistler group-velocity dispersion near the electron cyclotron frequency (ω ≤ ω_H). The results can be used to interpret the spectral shapes of the signals received from the Earth’s magnetosphere and ionosphere in the electron and ion whistler frequency ranges.     

Periodic perturbation of ambiguous figure: A neural-network model and a non-simulated experiment

Summary A neural-network model of the phenomenon of perceptual bistability in the presence of ambiguous figure is studied under the influence of a weak periodic perturbation. Computer simulations of the dynamical behaviour of the network show all the main characteristics of stochastic resonance. Preliminary results of a non-simulated experiment show a high degree of synchronization between the external modulation and the perceptual fluctuations. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.