Generation of on-off intermittency based on RSssler chaotic system

In this paper, one-state on-off intermittency and two-state on-off intermittency are generated in two five- dimensional continuum systems respectively. In each system, a two-dimensional subsystem is driven by the Rossler chaotic system. The parameter conditions under which the on-off intermittency occurs are discussed in detail. The statistical property of the intermittency is investigated. It is shown that the distribution of the laminar phase duration time follows a power law with an exponent of -3/2, which is a signature of on-off intermittency. Moreover, the phenomenon of intermingled basins is observed when attractors in the two symmetric invariant subspaces are stable. We provide an effective way to generate on-off intermittency based on a chaotic system, which is important for application and theoretical study.     

Analysis and circuit realization of intermittency with multiple laminar states

In this Letter, an electrical circuit is built for realizing the multi-state intermittency generated by a simple force-driven chaotic system. The intermittency phenomenon and its underlaying mechanism are analyzed, and the experimental results are discussed. It is shown that, with two classes of invariant subspaces, the number of the laminar states and the distance between the adjacent laminar states of the created multi-state on-off intermittency can be arbitrarily changed by manipulating the control parameters.     

Chaotic transition of random dynamical systems and chaos synchronization by common noises

We studied the mechanism behind the connection between the transition to chaos of random dynamical systems and the synchronization of chaotic maps driven by external common noises. Near the chaotic transition, the spatial size of random dynamical systems shows an extreme intermittent behavior. By calculating the scaling exponents, we have found that the origin of this intermittent behavior is on-off intermittency. This led us to conclude that chaotic transitions through on-off intermittency can be regarded as a route for random dynamical systems. To clarify this argument, a two-dimensional random dynamical system and two coupled logistic maps driven by external common noises were analyzed.     

Spatial orders appearing at instabilities of synchronous chaos of spatiotemporal systems

Various spatial orders introduced by the instabilities of synchronous chaotic state of spatiotemporal systems are investigated by considering coupled map lattice and chaotic partial differential equation. In particular, the motions of on-off intermittent states at the onset of the instabilities are studied in detail. The chaotic desynchronized patterns can be described by a simple universal form, including three parts: the synchronous chaos; a spatially ordered pattern, determined by the unstable mode of the reference synchronous chaos; and on-off intermittency of the scale of this given pattern. Received 31 July 2002 / Received in final form 20 November 2002 Published online 31 December 2002     

Hyperchaos--chaos--Hyperchaos Transition in a Class of On--Off Intermittent Systems Driven by a Family of Generalized Lorenz Systems

Blowout bifurcation in nonlinear systems occurs when a chaotic attractor lying in some symmetric subspace becomes transversely unstable. A class of five-dimensional continuous autonomous systems is considered, in which a two-dimensional subsystem is driven by a family of generalized Lorenz systems. The systems have some common dynamical characters. As the coupling parameter changes, blowout bifurcations occur in these systems and brings on change of the systems＇ dynamics. After the bifurcation the phenomenon of on-off intermittency appears. It is observed that the systems undergo a symmetric hyperchaos-chaos-hyperchaos transition via or after blowout bifurcations. An example of the systems is given, in which the drive system is the Chen system. We investigate the dynamical behaviour before and after the blowout bifurcation in the systems and make an analysis of the transition process. It is shown that in such coupled chaotic continuous systems, blowout bifurcation leads to a transition from chaos to hyperchaos for the whole systems, which provides a route to hyperchaos.     

On-off intermittency in continuum systems driven by Lorenz system

Previous studies of on-off intermittency in continuum systems are generally in the synchronization of identical chaotic oscillators or in the nonlinear systems driven by the Duffing oscillator. In this paper, one-state on-off intermittency and two-state on-off intermittency are observed in two five-dimensional continuum systems, respectively. The systems have skew product structure in which a two-dimensional subsystem is driven by the well-known Lorenz chaotic system. Moreover, the phenomenon of intermingled basins is observed below the blowout bifurcation. The statistical properties of the intermittency in the systems are investigated. It is shown that the distribution of the laminar phase duration time follows a power law, and that of the burst phase amplitude shows a −1 power law, which coincide with the basic statistical characteristics of on-off intermittency.     

一类新的混沌神经放电的动力学特征的实验和数学模型研究

神经元电活动理论模型Hindmarsh-Rose(HR)模型提示有位于周期1和周期2放电模式之间的一类特殊的混沌放电,但长期以来对其没有获得足够认识.依据回归映射的确定性结构和非线性预报的短期可预报性,确认了在大鼠的实验性神经起步点的实验中发现的位于周期1和周期2放电模式之间的非周期放电是混沌放电模式,还将该混沌放电模式区分为3个不同表观样式.其中1个表观形式与HR模型的仿真结果相类似,验证了HR模型的理论预期;其余2个样式与仿真结果并不相似.进一步揭示了3个表观样式的动力学特征以及相互之间的区别与联系,并与位于周期2和周期3节律之间、周期3和周期4节律之间的混沌比较了异同,也区别了从周期1到混沌再到周期2放电模式的节律转迁历程与其他的从周期1到周期2节律的分岔过程的不同.研究结果确认了该类特殊混沌节律和相应分岔过程的新特征,丰富了混沌放电节律和节律分岔序列的种类.还对仿真该混沌的多样性和非光滑特性,以及揭示该类混沌的产生途径等进行了讨论. 关键词： 混沌 神经放电模式 分岔 节律     

Intermittency near the phase boundary of chaotic synchronization in spatially extended systems

The intermittent behavior of spatially extended systems is investigated using the example of unidirectionally coupled Pierce diodes. It isshown that the same type of intermittency as in finite-scaled systems is characteristic of this system near the boundary of the chaotic phase synchronization regime, i.e., needle-eye type intermittency, which is in fact also equivalent to type I intermittency with noise in the supercritical region.     

Chaotic bursting as chaotic itinerancy in coupled neural oscillators

We show that chaotic bursting activity observed in coupled neural oscillators is a kind of chaotic itinerancy. In neuronal systems with phase deformation along the trajectory, diffusive coupling induces a dephasing effect. Because of this effect, an antiphase synchronized solution is stable for weak coupling, while an in-phase solution is stable for very strong coupling. For intermediate coupling, a chaotic bursting activity is generated. It is a mixture of three different states: an antiphase firing state, an in-phase firing state, and a nonfiring resting state. As we construct numerically the deformed torus manifold underlying the chaotic bursting state, it is shown that the three unstable states are connected to give rise to a global chaotic itinerancy structure. Thus we claim that chaotic itinerancy provides an alternative route to chaos via torus breakdown.     

可兴奋性细胞混沌放电区间的识别机理

在神经起步点记录到加周期分岔过程的生理实验数据，在对此分岔过程中位于周期n爆发 和周期(n+1)爆发之间的混沌的峰峰间期数据检测不稳定的周期轨道时，发现从靠近周期 n爆发的混沌的峰峰间期数据中，可以检测出不稳定的周期n轨道；而从靠近周期(n+1)爆 发的混沌的峰峰间期数据中，不仅可以检测出不稳定的周期(n+1)轨道，还可以检测出不稳 定的周期n轨道.针对该现象，借助于Sherman建议的胰腺β细胞模型，从非线性动力 学角度给出了理论解释.指明了由鞍结分岔和倍周期分岔分别产生第一类阵发和第三类阵发 为出现该 关键词： 峰峰间期 不稳定的周期轨道 鞍结分岔 倍周期分岔     

Non-Smooth Bifurcation and Chaos in a DC-DC Buck Converter

A direct-current-direct-current （DC-DC） buck converter with integrated load current feedback is studied with three kinds of Poincaré maps. The external corner-collision bifurcation occurs when the crossing number per period varies, and the internal corner-collision bifurcations occur along with period-doubling and period-tripling bifurcations in this model. The multi-band chaos roots in external corner-collision bifurcation and often grows into 1-band chaos. A new kind of chaotic sliding orbits, which is more complex for non-smooth systems, is also found in this model.     

Intermittency at the Boundary of Generalized Synchronization in Mutually Coupled Systems with Complex Attractor Topology

Technical Physics - The mechanisms of occurrence and characteristics of intermittency at the boundary of generalized synchronization in mutually coupled systems with complex (two-sheet) chaotic...     

Hénon映射的噪声诱导间歇现象及其临界值估算研究

本文研究了Hénon映射在噪声诱导下发生的间歇现象.通过数值模拟和全局分析手段,揭示了噪声诱导间歇现象的机理.基于随机敏感度函数法,通过检测噪声作用下周期吸引子的置信椭圆与混沌鞍的碰撞情况,给出了诱发间歇现象的噪声强度临界值的估算方法.结果表明,Hénon映射中噪声诱导间歇现象是由随机周期吸引子和混沌鞍不稳定流形的相互作用引发,随机敏感度函数的方法可以较好地估算发生间歇现象的噪声强度临界值.     

Type-I intermittency with noise versus eyelet intermittency

In this Letter we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency taking place in the vicinity of the chaotic phase synchronization boundary) supposed hitherto to be different phenomena. We show that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is confirmed by the consideration of different sample systems, such as quadratic map, Van der Pol oscillator and Rössler system. Consideration of the problem concerning the upper boundary of the intermittent behavior also confirms the validity of the statement on the equivalence of type-I intermittency in the presence of noise and eyelet intermittency observed in the onset of phase synchronization.     

Chaotic transition in a three-coupled phase-locked loop system

The chaotic transition is observed in a three-coupled phase-locked loop (PLL) system in both experiments and numerical simulations. In this system, three PLL oscillators are connected with the periodic boundary condition. Intermittency is found in partially synchronized phase, in which two of three oscillators synchronize with each other and form a pair, and the chaotic transition occurs due to the recombination of synchronized pairs so that different pair is re-formed. In this phase, on-off intermittency is also observed and statistical analyses are carried out for on-off intermittent time series. This intermittency is considered as a hybrid type of intermittency with both on-off intermittency and intermittency due to the recombination of synchronized pairs present in the same time series. We also show the chaotic transition phenomena in a three-coupled logistic map system. (c) 2001 American Institute of Physics.     

Periodic orbit analysis at the onset of the unstable dimension variability and at the blowout bifurcation

Many chaotic dynamical systems of physical interest present a strong form of nonhyperbolicity called unstable dimension variability (UDV), for which the chaotic invariant set contains periodic orbits possessing different numbers of unstable eigendirections. The onset of UDV is usually related to the loss of transversal stability of an unstable fixed point embedded in the chaotic set. In this paper, we present a new mechanism for the onset of UDV, whereby the period of the unstable orbits losing transversal stability tends to infinity as we approach the onset of UDV. This mechanism is unveiled by means of a periodic orbit analysis of the invariant chaotic attractor for two model dynamical systems with phase spaces of low dimensionality, and seems to depend heavily on the chaotic dynamics in the invariant set. We also described, for these systems, the blowout bifurcation (for which the chaotic set as a whole loses transversal stability) and its relation with the situation where the effects of UDV are the most intense. For the latter point, we found that chaotic trajectories off, but very close to, the invariant set exhibit the same scaling characteristic of the so-called on-off intermittency.     

A new deterministic model for chaotic reversals

We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced by crisis-induced intermittency, following a mechanism different from what is generally observed in similar deterministic models. Despite its simplicity, this system therefore generates a rich dynamics, able to model more complex physical systems. In particular, a comparison with reversals of the magnetic field of the Earth shows a surprisingly good agreement, and highlights the relevance of deterministic chaos to describe geomagnetic field dynamics.     

用多项式和阶跃函数构造网格多涡卷混沌吸引子及其电路实现

提出一种利用多项式和阶跃函数构造N×M涡卷的构造方法.利用蔡氏电路,传统的利用多项式函数只能产生双涡卷、三涡卷,在此基础上,通过多项式平移得到相空间x方向的多涡卷,再通过多项式与阶跃函数组合来扩展相空间中指标2的鞍焦平衡点,使得多涡卷向y方向延伸,从而生成网格多涡卷混沌吸引子.该构造方法的主要特征是通过光滑曲线和非光滑曲线的组合生成网格多涡卷混沌吸引子,能通过调整自然数N和M的值实现平面网格任意涡卷混沌吸引子阵列.理论分析、数值模拟和电路仿真证实了方法的可行性. 关键词： 网格多涡卷混沌吸引子 蔡氏电路 阶跃函数 电路实现     

Noise-induced intermittency in the quasiperiodic regime of Rayleigh-Bénard convection

Thermal measurements on a converting dilute³He-superfluid⁴He solution in the quasiperiodic regime show a transition from a mode-locked periodic state to chaotic time dependence via intermittency. The type of intermittency is discussed in the context of standard models of the phenomenon. In a region just below the onset of intermittency, injection of external multiplicative noise with noise amplitude above a certain threshold level induces the chaotic state. This noise-induced transition can be understood to be due to perturbations of a system with a barely stable attractor; the noise causes the system to escape the weakly attracting periodic points. We present a numerical simulation of a 1D map with external noise which explains some aspects of the noise-induced behavior, and a 2D map which has certain features of the intermittency.     

Phase synchronization of chaotic intermittent oscillations

We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization.