共查询到20条相似文献,搜索用时 31 毫秒
1.
We explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by Lorenz to study fundamental issues regarding the forecasting of spatially extended chaotic systems such as the atmosphere. First, we explore the spatiotemporal chaos limit by increasing the system size while holding the magnitude of the external forcing constant. Second, we explore the strong driving limit by increasing the external forcing while holding the system size fixed. As the system size is increased for small values of the forcing we find dynamical states that alternate between periodic and chaotic dynamics. The windows of chaos are extensive, on average, with relative deviations from extensivity on the order of 20%. For intermediate values of the forcing we find chaotic dynamics for all system sizes past a critical value. The fractal dimension exhibits a maximum deviation from extensivity on the order of 5% for small changes in system size and the deviation from extensivity decreases nonmonotonically with increasing system size. The length scale describing the deviations from extensivity is consistent with the natural chaotic length scale in support of the suggestion that deviations from extensivity are due to the addition of chaotic degrees of freedom as the system size is increased. We find that each wavelength of the deviation from extensive chaos contains on the order of two chaotic degrees of freedom. As the forcing is increased, at constant system size, the dimension density grows monotonically and saturates at a value less than unity. We use this to quantify the decreasing size of chaotic degrees of freedom with increased forcing which we compare with spatial features of the patterns. 相似文献
2.
In this Letter, the effects of random shortcuts in an array of coupled nonlinear chaotic pendulums and their ability to control the dynamical behavior of the system are investigated. We show that random shortcuts can induce periodic synchronized spatiotemporal motions, even though all oscillators are chaotic when uncoupled. This process exhibits a nonmonotonic dependence on the density of shortcuts. Specifically, there is an optimal amount of random shortcuts, which can induce the most ordered motion characterized by the largest order parameter that is introduced to measure the spatiotemporal order. Our results imply that topological randomness can tame spatiotemporal chaos. 相似文献
3.
本文研究了运动光格中原子间呈排斥作用的玻色-爱因斯坦凝聚系统的混沌时空动力学。通过理论分析,我们得到了具有简单零点的Melnikov函数,这表明系统存在Smale马蹄混沌。数值模拟显示,在一定的参数条件下,光格势强度的增大或s波散射长度的减小,都将迫使系统由规则状态进入混沌状态。 相似文献
4.
A novel image block cryptosystem based ona spatiotemporal chaotic system and a chaotic neural network 下载免费PDF全文
In this paper, we propose a novel block cryptographic scheme based on a spatiotemporal chaotic system and a chaotic neural network (CNN). The employed CNN comprises a 4-neuron layer called a chaotic neuron layer (CNL), where the spatiotemporal chaotic system participates in generating its weight matrix and other parameters. The spatiotemporal chaotic system used in our scheme is the typical coupled map lattice (CML), which can be easily implemented in parallel by hardware. A 160-bit-long binary sequence is used to generate the initial conditions of the CML. The decryption process is symmetric relative to the encryption process. Theoretical analysis and experimental results prove that the block cryptosystem is secure and practical, and suitable for image encryption. 相似文献
5.
In this paper we proposed a spatial modulated two-variable Martiel-Goldbeter model to describe the complex spatiotemporal disorder dynamical behavior during development of Dictyostelium discoideum strain FR17. As the nonlinear modulated parameter A and diffusion coefficient E varied, the system shows: 1) multiperiodic phase, 2) co-existence phase of chaotic and multi-periodic state, 3) spatiotemporal chaotic phase, 4) co-existence phase of chaotic, multi-periodic and steady state, and 5) co-existence phase of chaotic and steady state. These phases can be described by spatiotemporal power spectra, pattern distribution function and Lyapunov spectra. We believed that the complex spatiotemporal disorder dynamical behavior during development of Dictyosteliurn discoideum strain FR17 is a spatiotemporal chaotic state. 相似文献
6.
Nonattracting chaotic sets (chaotic saddles) are shown to be responsible for transient and intermittent dynamics in an extended system exemplified by a nonlinear regularized long-wave equation, relevant to plasma and fluid studies. As the driver amplitude is increased, the system undergoes a transition from quasiperiodicity to temporal chaos, then to spatiotemporal chaos. The resulting intermittent time series of spatiotemporal chaos displays random switching between laminar and bursty phases. We identify temporally and spatiotemporally chaotic saddles which are responsible for the laminar and bursty phases, respectively. Prior to the transition to spatiotemporal chaos, a spatiotemporally chaotic saddle is responsible for chaotic transients that mimic the dynamics of the post-transition attractor. 相似文献
7.
8.
We describe a wavelet-based approach to the investigation of spatiotemporally complex dynamics, and show through extensive numerical studies that the dynamics of the Kuramoto-Sivashinsky equation in the spatiotemporally chaotic regime may be understood in terms of localized dynamics in both space and scale (wave number). A projection onto a spline wavelet basis enables good separation of scales, each with characteristic dynamics. At the large scales, one observes essentially slow Gaussian dynamics; at the active scales, structured "events" reminiscent of traveling waves and heteroclinic cycles appear to dominate; while the strongly damped small scales display intermittent behavior. The separation of scales and their dynamics is invariant as the length of the system increases, providing additional support for the extensivity of the spatiotemporally complex dynamics claimed in earlier works. We show also that the dynamics are spatially localized, discuss various correlation lengths, and demonstrate the existence of a characteristic interaction length for instantaneous influences. Our results motivate and advance the search for localized, low-dimensional models that capture the full behavior of spatially extended chaotic partial differential equations. (c) 1999 American Institute of Physics. 相似文献
9.
An image encryption scheme based on new spatiotemporal chaos 总被引:1,自引:0,他引:1
Spatiotemporal chaos is chaotic dynamics in spatially extended system, which has attracted much attention in the image encryption field. The spatiotemporal chaos is often created by local nonlinearity dynamics and spatial diffusion, and modeled by coupled map lattices (CML). This paper introduces a new spatiotemporal chaotic system by defining the local nonlinear map in the CML with the nonlinear chaotic algorithm (NCA) chaotic map, and proposes an image encryption scheme with the permutation-diffusion mechanism based on these chaotic maps. The encryption algorithm diffuses the plain image with the bitwise XOR operation between itself pixels, and uses the chaotic sequence generated by the NCA map to permute the pixels of the resulting image. Finally, the constructed spatiotemporal chaotic sequence is employed to diffuse the shuffled image. The experiments demonstrate that the proposed encryption scheme is of high key sensitivity and large key space. In addition, the scheme is secure enough to resist the brute-force attack, entropy attack, differential attack, chosen-plaintext attack, known-plaintext attack and statistical attack. 相似文献
10.
Different transient-chaos related phenomena of spatiotemporal systems are reviewed. Special attention is paid to cases where spatiotemporal chaos appears in the form of chaotic transients only. The asymptotic state is then spatially regular. In systems of completely different origins, ranging from fluid dynamics to chemistry and biology, the average lifetimes of these spatiotemporal transients are found, however, to grow rapidly with the system size, often in an exponential fashion. For sufficiently large spatial extension, the lifetime might turn out to be larger than any physically realizable time. There is increasing numerical and experimental evidence that in many systems such transients mask the real attractors. Attractors may then not be relevant to certain types of spatiotemporal chaos, or turbulence. The observable dynamics is governed typically by a high-dimensional chaotic saddle. We review the origin of exponential scaling of the transient lifetime with the system size, and compare this with a similar scaling with system parameters known in low-dimensional problems. The effect of weak noise on such supertransients is discussed. Different crisis phenomena of spatiotemporal systems are presented and fractal properties of the chaotic saddles underlying high-dimensional supertransients are discussed. The recent discovery according to which turbulence in pipe flows is a very long lasting transient sheds new light on chaotic transients in other spatially extended systems. 相似文献
11.
Spatiotemporal communication with synchronized optical chaos 总被引:2,自引:0,他引:2
We propose a model system that allows communication of spatiotemporal information using an optical chaotic carrier waveform. The system is based on broad-area nonlinear optical ring cavities, which exhibit spatiotemporal chaos in a wide parameter range. Message recovery is possible through chaotic synchronization between transmitter and receiver. Numerical simulations demonstrate the feasibility of the proposed scheme, and the benefit of the parallelism of information transfer with optical wave fronts. 相似文献
12.
13.
Emergence of spatiotemporal chaos arising from far-field breakup of spiral waves in the plankton ecological systems 下载免费PDF全文
It has been reported that the minimal spatially extended
phytoplankton--zooplankton system exhibits both temporal
regular/chaotic behaviour, and spatiotemporal chaos in a patchy
environment. As a further investigation by means of computer
simulations and theoretical analysis, in this paper we observe that
the spiral waves may exist and the spatiotemporal chaos emerge when
the parameters are within the mixed Turing--Hopf bifurcation region,
which arises from the far-field breakup of the spiral waves over a
large range of diffusion coefficients of phytoplankton and
zooplankton. Moreover, the spatiotemporal chaos arising from the
far-field breakup of spiral waves does not gradually invade the
whole space of that region. Our results are confirmed by nonlinear
bifurcation of wave trains. We also discuss ecological implications
of these spatially structured patterns. 相似文献
14.
A time series from a human electroencephalogram (EEG) is used as a local perturbation to a reaction-diffusion model with spatiotemporal chaos. For certain finite ranges of amplitude and frequency it is observed that the strongly irregular perturbations can induce transient coherence in the chaotic system. This could be interpreted as "on-line" detection of an inherently correlated pattern embedded in the EEG. 相似文献
15.
Analysis of chaotic saddles in high-dimensional dynamical systems: the Kuramoto-Sivashinsky equation
This paper presents a methodology to study the role played by nonattracting chaotic sets called chaotic saddles in chaotic transitions of high-dimensional dynamical systems. Our methodology is applied to the Kuramoto-Sivashinsky equation, a reaction-diffusion partial differential equation. The paper describes a novel technique that uses the stable manifold of a chaotic saddle to characterize the homoclinic tangency responsible for an interior crisis, a chaotic transition that results in the enlargement of a chaotic attractor. The numerical techniques explained here are important to improve the understanding of the connection between low-dimensional chaotic systems and spatiotemporal systems which exhibit temporal chaos and spatial coherence. 相似文献
16.
Sensitivity of intrinsic mode functions of Lorenz system to initial values based on EMD method 下载免费PDF全文
Extreme sensitivity to initial values is an intrinsic character of
chaotic systems. The evolution of a chaotic system has a
spatiotemporal structure containing quasi-periodic changes of
different spatiotemporal scales. This paper uses an empirical mode
decomposition (EMD) method to decompose and compare the evolution of
the time-dependent evolutions of the $x$-component of the Lorenz system.
The results indicate that the sensitivity of
intrinsic mode function (IMF) component is dependent on initial
values, which provides some scientific evidence for the possibility
of long-range climatic prediction. 相似文献
17.
Based on the spatiotemporal chaotic system,a novel algorithm for constructing a one-way hash function is proposed and analysed.The message is divided into fixed length blocks.Each message block is processed by the hash compression function in parallel.The hash compression is constructed based on the spatiotemporal chaos.In each message block,the ASCII code and its position in the whole message block chain constitute the initial conditions and the key of the hash compression function.The final hash value is generated by further compressing the mixed result of all the hash compression values.Theoretic analyses and numerical simulations show that the proposed algorithm presents high sensitivity to the message and key,good statistical properties,and strong collision resistance. 相似文献
18.
《Physics letters. A》2006,349(6):467-473
An approach to generate multiple pseudorandom-bit sequences from a single spatiotemporal chaotic system is proposed in this Letter. A coupled map lattice is adopted as a prototype of a spatiotemporal chaotic system. The cryptographic properties of the pseudorandom-bit generator based on the coupled map lattice (CML–MPRBG) are analyzed. It is observed from simulation results that the CML–MPRBG has good cryptographic properties. Basic security analysis of a stream cipher based on the CML–MPRBG is also discussed. The results show that the CML–MPRBG can be a good candidate for constructing a secure cipher. 相似文献
19.
对Pecora和Carroll的混沌自同步方案的延迟同步误差进行了研究.在计算机上对Lorenz混沌系统伪装的延迟同步误差进行了模拟:给定系统参数,对应不同延迟时间,得出了均方误差与采样步长的关系曲线;给定系统参数和延迟时间,对应不同采样步长,得到了混沌时间序列的误差曲线;给定采样步长,对应不同的系统参数,获得了混沌时间序列的尺度效应和均方误差与采样步长的关系曲线.提出了减小延迟同步误差的一些方法,得到一些对混沌同步和混沌控制应用有意义的结果.
关键词:
混沌同步
时间同步
误差分析 相似文献
20.
Spatial orders appearing at instabilities of synchronous chaos of spatiotemporal systems 总被引:1,自引:0,他引:1
Shihong Wang Jinghua Xiao Xingang Wang Bambi Hu Gang Hu 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(4):571-575
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 相似文献