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A method of estimating initial conditions of coupled map lattices based on time-varying symbolic dynamics

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Chinese Physics B 2009年第5期18卷 1761-1768页

作者：沈民奋刘英林兰馨 College of Engineering Shantou University Department of Electronic Engineering City University of Hong Kong

A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer-Rao lower bound （CRLB） than that with the time-invariant estimation method, especially at high signal-to-noise ratios （SNRs）.

关键词： coupled map lattices symbolic dynamics initial condition estimation

Control of cascading failures in coupled map lattices based on adaptive predictive pinning control

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Journal of Zhejiang University-Science C(Computers and Electronics) 2011年第10期12卷 828-835页

作者： Zhe-jing BAO Gang WU Wen-jun YAN School of Electrical Engineering Zhejiang University Hangzhou 310027 China

An adaptive predictive pinning control is proposed to suppress the cascade in coupled map lattices (CMLs).Two monitoring strategies are applied:(1) A specific fraction of nodes with the highest degree or betweenness are chosen to constitute the set of monitored nodes;(2) During the cascade,an adaptive pinning control is implemented,in which only the nodes in the monitored set whose current state is normal but whose predictive state is abnormal,are pinned with the predictive *** show that for the scale-free (SF) CML the degree-based monitoring strategy is advantageous over the betweenness-based strategy,while for the small-world (SW) CML the situation is the *** the adaptive predictive pinning control,the fewer local controllers can effectively suppress the cascade throughout the whole network.

关键词： coupled map lattices Cascade Pinning Predictive control Degree Betweenness

A Cryptographic Scheme Based on Spatiotemporal Chaos of coupled map lattices

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Communications in Theoretical Physics 2006年第3期45卷 477-482页

作者： MA Hui CHEN Tian-Lun Institute of Physics Nankai University Tianjin 300071 China CCAST （World Laboratory） P.O. Box 8730 Beijing 100080 China

We propose a cryptographic scheme based on spatiotemporal chaos of coupled map lattices （CIVIL） ,which is based on one-time pad. The structure of the cryptosystem determines that the progress in decryption implies the progress in exploring the dynamical behavior of spatiotemporal chaos in CML. A part of the initial condition of CML is used as a secret key, and the recovery of the secret key by exhaustive search is impossible due to the sensitivity to the initial condition in spatiotemporal chaos system. Specially the software implementation of the scheme is easy.

关键词： spatiotemporal chaos coupled map lattices cryptography

Experimental system of coupled map lattices

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Frontiers of physics 2015年第3期10卷 101-104页

作者： Yu-Han Ma Lan-Qing Huang Chu-Min Sun Xiao-Wen Li Department of Physics Beijing Normal University Beijing 100875 China

We design an optical feedback loop system consisting of a liquid-crystal spatial light modulator （SLM）, a lens, polarizers, a CCD camera, and a computer. The system images every SLM pixel onto one camera pixel. The light intensity on the camera pixel shows a nonlinear relationship with the phase shift applied by the SLM. Every pixel behaves as a nonlinear map, and we can control the interaction of pixels. Therefore, this feedback loop system can be regarded as a spatially extended system. This experimental coupled map has variable dimensions, which can be up to 512 by 512. The system can be used to study high-dimensional problems that computer simulations cannot handle.

关键词： coupled map lattices photoelectric feedback loop

Chimera states in Gaussian coupled map lattices

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Frontiers of physics 2018年第2期13卷 39-42页

作者： Xiao-Wen Li Ran Bi Yue-Xiang Sun Shuo Zhang Qian-Qian Song Department of Physics Beijing Normal University Beijing 100875 China

We study chimera states in one-dimensional and two-dimensional Gaussian coupled map lattices through simulations and experiments. Similar to the case of global coupling oscillators, individual lattices can be regarded as being controlled by a common mean field. A space-dependent order pa- rameter is derived from a self-consistency condition in order to represent the collective state.

关键词： chimera state coupled map lattices nonlocal coupling

Periodic Windows in Weakly coupled map lattices

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Communications in Theoretical Physics 2008年第3期49卷 669-672页

作者： GAO Ji-Hua ZHAN Meng Wuhan Institute of Physics and Mathematics The Chinese Academy of Sciences Wuhan 430071 China Shenzhen Key Laboratory of Special Functional Materials College of Materials Shenzhen University Shenzhen 518060 China

The periodic windows in weakly coupled map lattices with both diffusive and gradient couplings are studied. By using the mode analysis method, which reduces the behavior of the coupled systems to a few numbers of independent modes, we theoretically analyze the detailed structures of the periodic windows. We find that the gradient coupling greatly enlarges the width of the periodic windows, compared with the diffusive coupling.

关键词： periodic windows coupled map lattices mode analysis method

Discretization of coupled map lattices for a Stream Cipher

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Tsinghua Science and Technology 2011年第3期16卷 241-246页

作者：尹汝明袁坚杨秋华山秀明王希勤 Department of Electronic Engineering Tsinghua University

coupled map lattices （CML） have been recently used to construct ciphers. However, the complicated operations on real numbers make these CML-based ciphers difficult to analyze. This paper presents a new stream cipher with the discretized CML which operates on binary numbers. When discretizing the CML, the effective network structure is explicitly preserved to improve the confusion and diffusion. The proposed cipher can be easily analyzed using proper cryptographic techniques and has good security. The cipher has a strict lower bound on the period length of 264 and its key setup scheme achieves enough diffusion. The keystreams pass all of the NIST statistical randomness tests and have good randomness properties. In addition the cipher is resistant to the guess-and-determine attack.

关键词： stream cipher coupled map lattices confusion and diffusion discretization statistical test

Synchronizing spatiotemporal chaos in the coupled map lattices using nonlinear feedback functions

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Nuclear Science and Techniques 1997年第3期 1-7页

作者： Fang Jin Qing ( China Institute of Atomic Energy, Beijing 102413) M K Ali △ ( Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4, Canada)

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关键词： Nonlinear feedback functions Synchronization Spatiotemporal chaos coupled map lattices Noise effect

Some Chaotic Properties of a Kind of coupled map lattices

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Journal of Applied Mathematics and Physics 2020年第6期8卷 968-975页

作者： Xiaofang Yang Tianxiu Lu Guo Liu Department of Mathematics and Statistics Sichuan University of Science and Engineering Zigong China Artificial Intelligence Key Laboratory of Sichuan Province Zigong China

This paper is concerned with some chaotic properties of a kind of coupled map lattices, which is proposed by Kaneko. First, this research discussed the sensitivity, infinite sensitivity, transitivity, accessibility, densely Li-Yorke sensitivity and exact of coupled map lattices. Then, some sufficient conditions under which is Kato chaotic, positive entropy chaotic and Ruelle-Takens chaos are obtained.

关键词： coupled map lattices Sensitivity Chaos Accessibility