共查询到20条相似文献,搜索用时 31 毫秒
1.
W. L. Lu F. M. Atay J. Jost 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(3):399-406
Complexity of dynamical networks can arise not only from
the complexity of the topological structure but also from the time
evolution of the topology. In this paper, we study the synchronous
motion of coupled maps in time-varying complex networks both
analytically and numerically. The temporal variation is rather
general and formalized as being driven by a metric dynamical system.
Four network models are discussed in detail in which the
interconnections between vertices vary through time randomly. These
models are: 1) i.i.d. sequences of random graphs with fixed wiring
probability, 2) groups of graphs with random switches between the
individual graphs, 3) graphs with temporary random failures of
nodes, and 4) the meet-for-dinner model where the vertices are
randomly grouped. We show that the temporal variation and randomness
of the connection topology can enhance synchronizability in many
cases; however, there are also instances where they reduce
synchronizability. In analytical terms, the Hajnal diameter of the
coupling matrix sequence is presented as a measure for the
synchronizability of the graph topology. In topological terms, the
decisive criterion for synchronization of coupled chaotic maps is
that the union of the time-varying graphs contains a spanning tree. 相似文献
2.
During the last few years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wavefunction statistics. In the first part of this review we give a detailed introduction to the spectral theory of quantum graphs and discuss exact trace formulae for the spectrum and the quantum-to-classical correspondence. The second part of this review is devoted to the spectral statistics of quantum graphs as an application to quantum chaos. In particular, we summarize recent developments on the spectral statistics of generic large quantum graphs based on two approaches: the periodic-orbit approach and the supersymmetry approach. The latter provides a condition and a proof for universal spectral statistics as predicted by random-matrix theory. 相似文献
3.
We consider universal shot noise in ballistic chaotic cavities from a semiclassical point of view and show that it is due to action correlations within certain groups of classical trajectories. Using quantum graphs as a model system, we sum these trajectories analytically and find agreement with random-matrix theory. Unlike all action correlations which have been considered before, the correlations relevant for shot noise involve four trajectories and do not depend on the presence of any symmetry. 相似文献
4.
We present quantum graphs with remarkably regular spectral characteristics. We call them regular quantum graphs. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly solvable in terms of periodic orbits. We present analytical solutions for the spectrum of regular quantum graphs in the form of explicit and exact periodic orbit expansions for each individual energy level. 相似文献
5.
Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability density variations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measures and show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to the time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics. 相似文献
6.
We study global stability of synchronization in asymmetrically connected networks of limit-cycle or chaotic oscillators. We extend the connection graph stability method to directed graphs with node balance, the property that all nodes in the network have equal input and output weight sums. We obtain the same upper bound for synchronization in asymmetrically connected networks as in the network with a symmetrized matrix, provided that the condition of node balance is satisfied. In terms of graphs, the symmetrization operation amounts to replacing each directed edge by an undirected edge of half the coupling strength. It should be stressed that without node balance this property in general does not hold. 相似文献
7.
8.
9.
基于周期性极化铌酸锂晶体的线性电光效应耦合波理论,数值研究了电光调制对外部光反馈垂直腔表面发射激光器(VCSEL)输出矢量混沌偏振模的操控.研究结果表明,VCSEL输出的偏振度随着电光晶体的长度或施加于电光晶体的外电场强度成周期性转换,控制一定的施加外电场强度和晶体的长度,激光器的不同参数下引起初始混沌偏振态都可以转换为其他任意混沌偏振态.特别是合理选择一定的施加外电场强度或晶体长度,VCSEL输出的任意混沌偏振模可以转换为完全一致的两线性混沌偏振模(x和ŷ偏振),即两线性混沌偏振模的能量能够达到稳定和完全均衡. 相似文献
10.
11.
《Physics letters. A》2006,354(4):298-304
Usually, phase synchronization is studied in chaotic systems driven by either periodic force or chaotic force. In the present work, we consider frequency locking in chaotic Rössler oscillator by a special driving force from a dynamical system with a strange nonchaotic attractor. In this case, a transition from generalized marginal synchronization to frequency locking is observed. We investigate the bifurcation of the dynamical system and explain why generalized marginal synchronization can occur in this model. 相似文献
12.
构建了一种在混沌噪声背景下检测并恢复微弱脉冲信号的模型.首先,基于混沌信号的短期可预测性及其对微小扰动的敏感性,对观测信号进行相空间重构、建立局域线性自回归模型进行单步预测,得到预测误差,并利用假设检验方法从预测误差中检测观测信号中是否含有微弱脉冲信号.然后,对微弱脉冲信号建立单点跳跃模型,并融合局域线性自回归模型,构成双局域线性(DLL)模型,以极小化DLL模型的均方预测误差为目标进行优化,采用向后拟合算法估计模型的参数,并最终恢复出混沌噪声背景下的微弱脉冲信号.仿真实验结果表明本文所建的模型能够有效地检测并恢复出混沌噪声背景中的微弱脉冲信号. 相似文献
13.
近期文献中报道了在具有自适应反馈突触的神经元模型中,随着参数的变化,存在从两个共存吸引子到一个相连吸引子再到两个共存吸引子的混沌转化现象.本文对此模型进行了电路设计,同时对具有非单调激活函数功能的电路设计进行了细致的研究,并利用Electronic Workbench (EWB)软件对所设计的电路进行了仿真实验,研究了电路中的混沌现象,验证了所设计电路的动力学行为与通过数值模拟结果十分相似.
关键词:
自适应反馈突触
神经元模型
混沌
电路设计 相似文献
14.
M. J. Rebouças R. K. Tavakol A. F. F. Teixeira 《General Relativity and Gravitation》1998,30(4):535-543
We introduce the notion of topological fragility and briefly discuss some examples from the literature. An important example of this type of fragility is the way globally anisotropic Bianchi V generalisations of the FLRW k = –1 model result in a radical restriction on the allowed topology of spatial sections, thereby excluding compact cosmological models with negatively curved three-sections with anisotropy. An outcome of this is to exclude chaotic mixing in such models, which may be relevant, given the many recent attempts at employing compact FLRW k = –1 models to produce chaotic mixing in the cosmic microwave background radiation, if the Universe turns out to be globally anisotropic. 相似文献
15.
16.
考虑涨落作用下周期驱动的过阻尼分数阶棘轮模型, 通过模型的数值求解, 研究确定性棘轮的混沌特性与噪声的作用对输运行为的影响, 进而讨论过阻尼分数阶分子马达反向输运的机理. 分析表明: 随着势垒高度、 势不对称性与模型记忆性的变化, 随机棘轮的反向输运并不必然地要求确定性棘轮也反向输运; 随着模型阶数的减小, 亦即分数阻尼介质记忆性的增强, 确定性棘轮在反向输运之前会经历一个周期倍化导致的混沌状态, 但在噪声作用下, 反向流的发生会提前, 即混沌状态的确定性棘轮在噪声的作用下即可进行反向输运. 也就是说, 噪声能定性地改变棘轮的输运状态: 从无噪声时的混沌运动到有噪声时的定向输运. 这是过阻尼随机棘轮反向输运的一种机理, 也是噪声在定向输运过程中发挥积极作用的一个体现. 相似文献
17.
Different methods to utilize the rich library of patterns and behaviors of a chaotic system have been proposed for doing computation or communication. Since a chaotic system is intrinsically unstable and its nearby orbits diverge exponentially from each other, special attention needs to be paid to the robustness against noise of chaos-based approaches to computation. In this paper unstable periodic orbits, which form the skeleton of any chaotic system, are employed to build a model for the chaotic system to measure the sensitivity of each orbit to noise, and to select the orbits whose symbolic representations are relatively robust against the existence of noise. Furthermore, since unstable periodic orbits are extractable from time series, periodic orbit-based models can be extracted from time series too. Chaos computing can be and has been implemented on different platforms, including biological systems. In biology noise is always present; as a result having a clear model for the effects of noise on any given biological implementation has profound importance. Also, since in biology it is hard to obtain exact dynamical equations of the system under study, the time series techniques we introduce here are of critical importance. 相似文献
18.
提出了一种基于广义混沌映射切换的混沌同步保密通信方式.这种通信方式首先构建产生多种混沌序列的广义混沌映射模型,然后在不同时段根据切换策略产生不同混沌序列,在发送端,将信号与混沌载波之和取模运算后再嵌入混沌映射的输入端进行迭代运算以实现调制;在接收端,根据切换协议,用同一个相应的广义混沌映射模型从接收信号中提取混沌载波并进而恢复信息信号.研究结果表明:这种基于广义混沌映射切换的混沌同步通信方式比基于单一混沌系统的保密通信方式具有更强的抗干扰能力,保密性能更好,且实现简单.
关键词:
混沌
混沌映射切换
同步
保密通信 相似文献
19.
X. San Liang 《Entropy (Basel, Switzerland)》2021,23(6)
Causality analysis is an important problem lying at the heart of science, and is of particular importance in data science and machine learning. An endeavor during the past 16 years viewing causality as a real physical notion so as to formulate it from first principles, however, seems to have gone unnoticed. This study introduces to the community this line of work, with a long-due generalization of the information flow-based bivariate time series causal inference to multivariate series, based on the recent advance in theoretical development. The resulting formula is transparent, and can be implemented as a computationally very efficient algorithm for application. It can be normalized and tested for statistical significance. Different from the previous work along this line where only information flows are estimated, here an algorithm is also implemented to quantify the influence of a unit to itself. While this forms a challenge in some causal inferences, here it comes naturally, and hence the identification of self-loops in a causal graph is fulfilled automatically as the causalities along edges are inferred. To demonstrate the power of the approach, presented here are two applications in extreme situations. The first is a network of multivariate processes buried in heavy noises (with the noise-to-signal ratio exceeding 100), and the second a network with nearly synchronized chaotic oscillators. In both graphs, confounding processes exist. While it seems to be a challenge to reconstruct from given series these causal graphs, an easy application of the algorithm immediately reveals the desideratum. Particularly, the confounding processes have been accurately differentiated. Considering the surge of interest in the community, this study is very timely. 相似文献
20.
We obtain in a closed form the 1/N2 contribution to the free energy of the two Hermitian N×N random matrix model with nonsymmetric quartic potential. From this result, we calculate numerically the Yang–Lee zeros of the 2D Ising model on dynamical random graphs with the topology of a torus up to n=16 vertices. They are found to be located on the unit circle on the complex fugacity plane. In order to include contributions of even higher topologies we calculated analytically the nonperturbative (sum over all genus) partition function of the model
for the special cases of N=1,2 and graphs with n≤20 vertices. Once again the Yang–Lee zeros are shown numerically to lie on the unit circle on the complex fugacity plane. Our results thus generalize previous numerical results on random graphs by going beyond the planar approximation and strongly indicate that there might be a generalization of the Lee–Yang circle theorem for dynamical random graphs. 相似文献