In this paper, cascading failure is studied by coupled map lattice （CML） methods in preferential attachment community networks. It is found that external perturbation R is increasing with modularity Q growing by sim...In this paper, cascading failure is studied by coupled map lattice （CML） methods in preferential attachment community networks. It is found that external perturbation R is increasing with modularity Q growing by simulation. In particular, the large modularity Q can hold off the cascading failure dynamic process in community networks. Furthermore, different attack strategies also greatly affect the cascading failure dynamic process. It is particularly significant to control cascading failure process in real community networks.展开更多
This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods. The whole work focuses on investigating som...This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods. The whole work focuses on investigating some indices including the number of failed edges, dynamic edge tolerance capacity and the perturbation of edge. In general, it assumes that the perturbation is attributed to the normal distribution in adopted simulations. By investigating the effectiveness of edge tolerance in scale-free and random networks, it finds that the larger tolerance parameter λ can more efficiently delay the cascading failure process for scale-free networks than random networks. These results indicate that the cascading failure process can be effectively controlled by increasing the tolerance parameter λ. Moreover, the simulations also show that, larger variance of perturbation can easily trigger the cascading failures than the smaller one. This study may be useful for evaluating efficiency of whole traffic systems, and for alleviating cascading failure in such systems.展开更多
The partial and complete periodic synchronization in coupled discontinuous map lattices consisting of both discon- tinuous and non-invertible maps are discussed. We classify three typical types of periodic synchroniza...The partial and complete periodic synchronization in coupled discontinuous map lattices consisting of both discon- tinuous and non-invertible maps are discussed. We classify three typical types of periodic synchronization states, which give rise to different spatiotemporal patterns including static partial periodic synchronization, dynamically periodic syn- chronization, and complete periodic synchronization patterns. A special prelude dynamics of partial and complete periodic synchronization motion, which is shown by five separated concave curves in the time series plots of the order parameters, is observed. The detailed analysis shows that the special prelude dynamics is induced by the competition between two synchronized clusters, and the analytical expression for the corresponding order parameter is obtained.展开更多
In the paper, we study effects of scale-free （SF） topology on dynamical synchronization and control in coupled map lattices （CIVIL）. Our strategy is to apply three feedback control methods, including constant feed...In the paper, we study effects of scale-free （SF） topology on dynamical synchronization and control in coupled map lattices （CIVIL）. Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength γc for the first time-delayed feedback control is increased linearly as e is increased linearly. The GML with SF loses synchronization and intermittency occurs if γ 〉 γc. Numerical examples are presented to demonstrate all results.展开更多
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 t...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.展开更多
It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite arra...It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite array of coupled oscillators. A method for estimating the critical coupling strength below which these solutions with time period persist is given. For some particular nonlinear solutions with time period,exponential decay in space is proved.展开更多
Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping ...Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence （CD）. Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to- noise ratios （SNRs） are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors usiug symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.展开更多
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 s...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）.展开更多
We present a self-synchronizing stream encryption scheme based on one-dimensional coupled map lattices which is introduced as a model with the essential features of spatiotemporal chaos, and of great complexity and di...We present a self-synchronizing stream encryption scheme based on one-dimensional coupled map lattices which is introduced as a model with the essential features of spatiotemporal chaos, and of great complexity and diffusion capability of the little disturbance in the initial condition. To evaluate the scheme, a series of statistical tests are employed, and the results show good random-look nature of the ciphertext. Furthermore, we apply our algorithm to encrypt a grey-scale image to show the key sensitivity.展开更多
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 inde...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.展开更多
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, d...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 <img src="Edit_c0fc315a-d176-4c9e-9e41-5cb6bc6d679d.bmp" alt="" /> is Kato chaotic, positive entropy chaotic and Ruelle-Takens chaos are obtained.展开更多
Spatiotemporal chaos is studied by using the unidirectional traffic coupled lattice model with hyperbolic tangent local map. The coupled map lattice (CML) model can simulate the complex traffic flow phenomenon which i...Spatiotemporal chaos is studied by using the unidirectional traffic coupled lattice model with hyperbolic tangent local map. The coupled map lattice (CML) model can simulate the complex traffic flow phenomenon which is similar to the traditional traffic flow model. The nonlinear feedback method is used to study the control of the chaotic system of the unidirectionally traffic coupled map lattice model. The stability of spatiotemporal chaos in the coupled map lattice is realized. The results of numerical simulation show that there is a relationship between control results and control parameters when controlling spatiotemporal chaos to a uniform stable state in a certain phase space compression parameter region.展开更多
Based on the nonlinear theory, a secure watermarking algorithm using wavelet transform and coupled map lattice is presented. The chaos is sensitive to initial conditions and has a good non-relevant correlation propert...Based on the nonlinear theory, a secure watermarking algorithm using wavelet transform and coupled map lattice is presented. The chaos is sensitive to initial conditions and has a good non-relevant correlation property, but the finite precision effect limits its application in practical digital watermarking system. To overcome the undesirable short period of chaos mapping and improve the security level of watermarking, the hyper-chaotic sequence is adopted in this algorithm. The watermark is mixed with the hyper-chaotic sequence and embedded in the wavelet domain of the host image. Experimental results and analysis are given to demonstrate that the proposed watermarking algorithm is transparent, robust and secure.展开更多
A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid hows. It is found that the parameter region of spatio...A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid hows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid hows can be envisaged.展开更多
基金supported by National Basic Research Program of China (Grant No 2006CB705500)Changjiang Scholars and Innovative Research Team in University (Grant No IRT0605)the National Natural Science Foundation of China (Grant No 70631001)
文摘In this paper, cascading failure is studied by coupled map lattice （CML） methods in preferential attachment community networks. It is found that external perturbation R is increasing with modularity Q growing by simulation. In particular, the large modularity Q can hold off the cascading failure dynamic process in community networks. Furthermore, different attack strategies also greatly affect the cascading failure dynamic process. It is particularly significant to control cascading failure process in real community networks.
基金supported by National Basic Research Program of China (Grant No 2006CB705500)Chang-Jiang Scholars and Innovative Research Team in University of China (Grant No IRT0605)the National Natural Science Foundation of China (Grant No70631001)
文摘This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods. The whole work focuses on investigating some indices including the number of failed edges, dynamic edge tolerance capacity and the perturbation of edge. In general, it assumes that the perturbation is attributed to the normal distribution in adopted simulations. By investigating the effectiveness of edge tolerance in scale-free and random networks, it finds that the larger tolerance parameter λ can more efficiently delay the cascading failure process for scale-free networks than random networks. These results indicate that the cascading failure process can be effectively controlled by increasing the tolerance parameter λ. Moreover, the simulations also show that, larger variance of perturbation can easily trigger the cascading failures than the smaller one. This study may be useful for evaluating efficiency of whole traffic systems, and for alleviating cascading failure in such systems.
基金supported by the National Natural Science Foundation of China(Grant No.10875076)the Natural Science Foundation of Shaanxi Province,China(Grant No.SJ08A23)
文摘The partial and complete periodic synchronization in coupled discontinuous map lattices consisting of both discon- tinuous and non-invertible maps are discussed. We classify three typical types of periodic synchronization states, which give rise to different spatiotemporal patterns including static partial periodic synchronization, dynamically periodic syn- chronization, and complete periodic synchronization patterns. A special prelude dynamics of partial and complete periodic synchronization motion, which is shown by five separated concave curves in the time series plots of the order parameters, is observed. The detailed analysis shows that the special prelude dynamics is induced by the competition between two synchronized clusters, and the analytical expression for the corresponding order parameter is obtained.
基金The project supported by the Key Program of National Natural Science Foundation of China under Grant No. 70431002 and National Natural Science Foundation of China under Grant Nos. 70371068 and 10247005 The authors thank Drs. Atay and Chun-Guang Li for their useful advices and discussions.
文摘In the paper, we study effects of scale-free （SF） topology on dynamical synchronization and control in coupled map lattices （CIVIL）. Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength γc for the first time-delayed feedback control is increased linearly as e is increased linearly. The GML with SF loses synchronization and intermittency occurs if γ 〉 γc. Numerical examples are presented to demonstrate all results.
基金The project supported by National Natural Science Foundation of China under Grant No. 90203008 and the Doctoral Foundation of the Ministry of Education of China under Grant No. 2002055009
文摘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.
文摘It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite array of coupled oscillators. A method for estimating the critical coupling strength below which these solutions with time period persist is given. For some particular nonlinear solutions with time period,exponential decay in space is proved.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61072037 and 60271023)the Natural Science Foundation of Guangdong Province,China (Grant No. 10151503101000011)
文摘Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence （CD）. Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to- noise ratios （SNRs） are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors usiug symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.
基金supported by the National Natural Science Foundation of China(Grant Nos 60271023 and 60571066)the Natural Science Foundation of Guangdong Province,China(Grant Nos 5008317 and 7118382)
文摘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）.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 90203008 and 10547120 and the Doctoral Foundation of the Ministry of Education of China under Grant No. 2002055009
文摘We present a self-synchronizing stream encryption scheme based on one-dimensional coupled map lattices which is introduced as a model with the essential features of spatiotemporal chaos, and of great complexity and diffusion capability of the little disturbance in the initial condition. To evaluate the scheme, a series of statistical tests are employed, and the results show good random-look nature of the ciphertext. Furthermore, we apply our algorithm to encrypt a grey-scale image to show the key sensitivity.
基金supported by National Natural Science Foundation of China under Grants Nos.10675161,10405018,and 70571053
文摘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.
文摘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 <img src="Edit_c0fc315a-d176-4c9e-9e41-5cb6bc6d679d.bmp" alt="" /> is Kato chaotic, positive entropy chaotic and Ruelle-Takens chaos are obtained.
文摘Spatiotemporal chaos is studied by using the unidirectional traffic coupled lattice model with hyperbolic tangent local map. The coupled map lattice (CML) model can simulate the complex traffic flow phenomenon which is similar to the traditional traffic flow model. The nonlinear feedback method is used to study the control of the chaotic system of the unidirectionally traffic coupled map lattice model. The stability of spatiotemporal chaos in the coupled map lattice is realized. The results of numerical simulation show that there is a relationship between control results and control parameters when controlling spatiotemporal chaos to a uniform stable state in a certain phase space compression parameter region.
文摘Based on the nonlinear theory, a secure watermarking algorithm using wavelet transform and coupled map lattice is presented. The chaos is sensitive to initial conditions and has a good non-relevant correlation property, but the finite precision effect limits its application in practical digital watermarking system. To overcome the undesirable short period of chaos mapping and improve the security level of watermarking, the hyper-chaotic sequence is adopted in this algorithm. The watermark is mixed with the hyper-chaotic sequence and embedded in the wavelet domain of the host image. Experimental results and analysis are given to demonstrate that the proposed watermarking algorithm is transparent, robust and secure.
基金The study is supported by"Nonlinear Sciences Project"from the State Science and Technology Commission of China.
文摘A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid hows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid hows can be envisaged.
