共查询到20条相似文献,搜索用时 343 毫秒
1.
We show that it is possible to devise a large class of skew-product dynamical systems which have strange nonchaotic attractors
(SNAs): the dynamics is asymptotically on fractal attractors and the largest Lyapunov exponent is non-positive. Furthermore,
we show that quasiperiodic forcing, which has been a hallmark of essentially all hitherto known examples of such dynamics
is not necessary for the creation of SNAs. 相似文献
2.
A nonchaotic attractor is observed in an infinite-dimensional system which is related to optical bistability and described by a nonlinear time-delay differential equation. The observed nonchaotic attractor is characterized by the strange trajectory of attractor but with negative value for the largest Lyapunov exponent, as well as the Fourier power spectra. 相似文献
3.
Badard R 《Chaos (Woodbury, N.Y.)》2008,18(2):023127
Iterations on R given by quasiperiodic displacement are closely linked with the quasiperiodic forcing of an oscillator. We begin by recalling how these problems are related. It enables us to predict the possibility of appearance of strange nonchaotic attractors (SNAs) for simple increasing maps of the real line with quasiperiodic displacement. Chaos is not possible in this case (Lyapounov exponents cannot be positive). Studying this model of iterations on R for larger variations, beyond critical values where it is no longer invertible, we can get chaotic motions. In this situation we can get a lot of strange attractors because we are able to smoothly adjust the value of the Lyapounov exponent. The SNAs obtained can be viewed as the result of pasting pieces of trajectories, some of which having positive local Lyapounov exponents and others having negative ones. This leads us to think that the distinction between these SNAs and chaotic attractors is rather weak. 相似文献
4.
We study three critical curves in a quasiperiodically driven system with time delays, where occurrence of symmetry-breaking and symmetry-recovering phenomena can be observed. Typical dynamical tongues involving strange nonchaotic attractors (SNAs) can be distinguished. A striking phenomenon that can be discovered is multistability and coexisting attractors in some tongues surrounding by critical curves. The blowout bifurcation accompanying with on-off intermittency can also be observed. We show that collision of attractors at a symmetric invariant subspace can lead to the appearance of symmetry-breaking. 相似文献
5.
本文研究了准周期外力驱动下Lorenz系统的动力学行为,发现当外强迫的振幅达到某一个临界值时,系统的动力学行为将会发生根本性的变化,由此揭示了产生非混沌奇怪吸引子(Strange Nonchaotic Attractor, SNA)的一个新机制:准周期外强迫振幅的加大导致系统由奇怪的混沌吸引子转变为SNA,系统的相空间最终被压缩至一个准周期环上.并且本文的结果表明,外强迫的临界振幅与Lorenz系统Rayleigh数的大小成正比,而其受外强迫频率变化的影响并不大.
关键词:
准周期
Lorenz系统
非混沌奇怪吸引子 相似文献
6.
7.
The transitions from or to strange nonchaotic attractors are investigated by recurrence plot-based methods. The techniques
used here take into account the recurrence times and the fact that trajectories on strange nonchaotic attractors (SNAs) synchronize.
The performance of these techniques is shown for the Heagy-Hammel transition to SNAs and for the fractalization transition
to SNAs for which other usual nonlinear analysis tools are not successful.
相似文献
8.
Ngamga EJ Buscarino A Frasca M Fortuna L Prasad A Kurths J 《Chaos (Woodbury, N.Y.)》2008,18(1):013128
Numerous studies have shown that strange nonchaotic attractors (SNAs) can be observed generally in quasiperiodically forced systems. These systems could be one- or high-dimensional maps, continuous-time systems, or experimental models. Recently introduced measures of complexity based on recurrence plots can detect the transitions from quasiperiodic to chaotic motion via SNAs in the previously cited systems. We study here the case of continuous-time systems and experimental models. In particular, we show the performance of the recurrence measures in detecting transitions to SNAs in quasiperiodically forced excitable systems and experimental time series. 相似文献
9.
We discuss strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors in a quasiperiodically driven system with time delays. A route and the associated mechanism are described for a special type of attractor called strange-nonchaotic-attractor-like (SNA-like) through T2 torus bifurcation. The type of attractor can be observed in large parameter domains and it is easily mistaken for a true SNA judging merely from the phase portrait, power spectrum and the largest Lyapunov exponent. SNA-like attractor is not strange and has no phase sensitivity. Conditions for Neimark-Sacker bifurcation are obtained by theoretical analysis for the unforced system. Complicated and interesting dynamical transitions are investigated among the different tongues. 相似文献
10.
《Physics letters. A》1999,259(5):355-365
We describe a type of intermittency present in a strange nonchaotic attractor of a quasiperiodically forced system. This has a similar scaling behaviour to the intermittency found in an attractor-merging crisis of chaotic attractors. By studying rational approximations to the irrational forcing we present a reasoning behind this scaling, which also provides insight into the mechanism which creates the strange nonchaotic attractor. 相似文献
11.
The dynamics of a modified logistic mapping are considered for a system with the order parameter modulated by an external
signal. It is shown that the Kolmogorov-Sinay entropy changes with changing modulation depth, while the harmonic signals and
white noise can be used as a modulating signal. The conditions for the excitation of regular and strange nonchaotic attractors
in the phase space are established. 相似文献
12.
E. Neumann A. Pikovsky 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,26(2):219-228
We consider the dynamics of the overdamped Josephson junction under the influence of an external quasiperiodic driving field.
In dependence on parameter values either a quasiperiodic motion or a strange nochaotic attractor (SNA) can be observed. The
latter corresponds to a resistive state in the current-voltage characteristics while for quasiperiodic motion a finite superconducting
current exists for zero voltage. It is shown that in the case of SNA a nonzero mean voltage across the junction can appear
due to symmetry breakings. Based on this observation a detailed symmetry consideration of the generalized equation of motion
is performed and symmetry conditions ensuring zero mean voltage across the junction are found.
Received 16 August 2001 and Received in final form 22 January 2002 相似文献
13.
Characterizing strange nonchaotic attractors 总被引:1,自引:0,他引:1
Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Second, we propose to characterize their strangeness by calculating a phase sensitivity exponent, that measures the sensitivity with respect to changes of the phase of the external force. It is shown that phase sensitivity appears if there is a nonzero probability for positive local Lyapunov exponents to occur. (c) 1995 American Institute of Physics. 相似文献
14.
A variety of different dynamical regimes involving strange nonchaotic attractors (SNAs) can be observed in a quasiperiodically forced delayed system. We describe some numerical experiments giving evidences of intertwined basin boundaries (smooth, non-Wada fractal and Wada property) for SNAs. In particular, we show that Wada property, fractality and smoothness can be intertwined on arbitrarily fine scales. This suggests that SNAs can exhibit the final state sensitivity and unpredictable behaviors. An interesting dynamical transition of SNAs together with associated mechanisms from non-Wada fractal to Wada intertwined basin boundaries is examined. A scaling exponent is used to characterize the intertwined basin boundaries. 相似文献
15.
Resonant perturbations are effective for harnessing nonlinear oscillators for various applications such as controlling chaos and inducing chaos. Of physical interest is the effect of small frequency mismatch on the attractors of the underlying dynamical systems. By utilizing a prototype of nonlinear oscillators, the periodically forced Duffing oscillator and its variant, we find a phenomenon: resonant-frequency mismatch can result in attractors that are nonchaotic but are apparently strange in the sense that they possess a negative Lyapunov exponent but its information dimension measured using finite numerics assumes a fractional value. We call such attractors pseudo-strange. The transition to pesudo-strange attractors as a system parameter changes can be understood analytically by regarding the system as nonstationary and using the Melnikov function. Our results imply that pseudo-strange attractors are common in nonstationary dynamical systems. 相似文献
16.
Whether strange nonchaotic attractors (SNAs) can occur typically in dynamical systems other than quasiperiodically driven systems has long been an open question. Here we show, based on a physical analysis and numerical evidence, that robust SNAs can be induced by small noise in autonomous discrete-time maps and in periodically driven continuous-time systems. These attractors, which are relevant to physical and biological applications, can thus be expected to occur more commonly in dynamical systems than previously thought. 相似文献
17.
We study the existence of strange nonchaotic attractors (SNA) in the family of Harper maps. We prove that for a set of parameters of positive measure, the map possesses a SNA. However, the set is nowhere dense. By changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a SNA. 相似文献
18.
S Rajasekar 《Pramana》1995,44(2):121-131
In this paper we investigate numerically the possibility of conversion of a chaotic attractor into a nonchaotic but strange
attractor in both a discrete system (an one dimensional map) and in a continuous dynamical system — Bonhoeffer—van der Pol
oscillator. In these systems we show suppression of chaotic property, namely, the sensitive dependence on initial states,
by adding appropriate i) chaotic signal and ii) Gaussian white noise. The controlled orbit is found to be strange but nonchaotic
with largest Lyapunov exponent negative and noninteger correlation dimension. Return map and power spectrum are also used
to characterize the strange nonchaotic attractor. 相似文献
19.
The object of investigation is a system consisting of two coupled nonautonomous van der Pol oscillators the characteristics frequencies of which differ by a factor of 2. The system is subjected to an external action in the form of slow periodic modulation of an oscillation-controlling parameter and also to an additional action at a frequency that is in an irrational relation with the modulation frequency. It is shown that the variation of the oscillation phase over a modulation period can be approximated by a 2D map on a torus that has a robust (structurally stable) Hunt-Ott strange nonchaotic attractor. Calculations of the quantitative characteristics of the attractor corresponding to the initial set of nonautonomous coupled oscillators (such as phase sensitivity exponent, structures and scaling of rational approximations, as well as Lyapunov exponents and their parameter dependence) confirm the presence of the Hunt-Ott strange nonchaotic attractor. 相似文献
20.
Whether Wada basins of strange nonchaotic attractors (SNAs) can exist has been an open problem. Here we verify the existence of Wada basin for SNAs in a quasiperiodically forced Duffing map. We show that the SNAs? basins are full Wada for a set of parameters of positive measure. We identify two types of SNAs? Wada basins by the basin cell method. It suggests that SNAs cannot be predicted reliably for the specific initial conditions. 相似文献