For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; ...For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; （2） No over-coarse graining preproeessing, such as transferring the original signal into a binary time series, is needed. Co complexity measure proposed by us previously is one of such measures. However, it lacks the solid mathematical foundation and thus its use is limited. A modified version of this measure is proposed, and some important properties are proved rigorously. According to these properties, this measure can be considered as an index of randomness of time series in some senses, and thus also a quantitative index of complexity under the meaning of randomness finding complexity. Compared with other similar measures, this measure seems more suitable for estimating a large quantity of complexity measures for a given task, such as studying the dynamic variation of such measures in sliding windows of a long process, owing to its fast speed for estimation.展开更多
This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors. The two networks can be undirected or directed, and they may also co...This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors. The two networks can be undirected or directed, and they may also contain isolated nodes and clusters. By using suitable controllers, sufficient conditions for finite-time generalized outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the synchronization time is also numerically demonstrated.展开更多
This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochast...This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochastic differential equations, sufficient conditions for the stability of the error dynamics are derived. Numerical simulations are also shown to demonstrate the effectiveness of these theoretic results.展开更多
This paper introduces a new three dimensional autonomous system with five equilibrium points. It demonstrates complex chaotic behaviours within a wide range of parameters, which are described by phase portraits, Lyapu...This paper introduces a new three dimensional autonomous system with five equilibrium points. It demonstrates complex chaotic behaviours within a wide range of parameters, which are described by phase portraits, Lyapunov exponents, frequency spectrum, etc. Analysis of the bifurcation and Poincar@ map is used to reveal mechanisms of generating these complicated phenomena. The corresponding electronic circuits are designed, exhibiting experimental chaotic attractors in accord with numerical simulations. Since frequency spectrum analysis shows a broad frequency bandwidth, this system has perspective of potential applications in such engineering fields as secure communication.展开更多
The new autonomous system with only three equilibrium points is introduced. This system does not belong to the generalized Lorenz systems. The novel attractors are observed over a large range of parameters, which have...The new autonomous system with only three equilibrium points is introduced. This system does not belong to the generalized Lorenz systems. The novel attractors are observed over a large range of parameters, which have rarely been reported in previous work. As an important component in chaotic signal generators, a physical circuit has been designed. The experimental results are in agreement with numerical simulations. More significantly, spectral analysis shows that the system has an extremely broad frequency spectral bandwidth in 0-131.6 Hz, without investigating any possible electronic techniques, which is more desirable for secure communications.展开更多
It was theoretically proved that one-dimensional transiently chaotic neural networks have chaotic structure in sense of Li-Yorke theorem with some given assumptions using that no division implies chaos. In particular,...It was theoretically proved that one-dimensional transiently chaotic neural networks have chaotic structure in sense of Li-Yorke theorem with some given assumptions using that no division implies chaos. In particular, it is further derived sufficient conditions for the existence of chaos in sense of Li- Yorke theorem in chaotic neural network, which leads to the fact that Aihara has demonstrated by numerical method. Finally, an example and numerical simulation are shown to illustrate and reinforce the previous theory.展开更多
In the present paper, the fractal rough surface is described by a band-limited Weierstrass-Mandelbrot function. By using the Monte Carlo method and optimal method, a minimal target function method is applied to invert...In the present paper, the fractal rough surface is described by a band-limited Weierstrass-Mandelbrot function. By using the Monte Carlo method and optimal method, a minimal target function method is applied to inverting the fractal dimension of the fractal rough surface. Numerical simulations show that the method can avoid the influence of the fractal characteristic scale, and that the method is of high precision.展开更多
文摘For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; （2） No over-coarse graining preproeessing, such as transferring the original signal into a binary time series, is needed. Co complexity measure proposed by us previously is one of such measures. However, it lacks the solid mathematical foundation and thus its use is limited. A modified version of this measure is proposed, and some important properties are proved rigorously. According to these properties, this measure can be considered as an index of randomness of time series in some senses, and thus also a quantitative index of complexity under the meaning of randomness finding complexity. Compared with other similar measures, this measure seems more suitable for estimating a large quantity of complexity measures for a given task, such as studying the dynamic variation of such measures in sliding windows of a long process, owing to its fast speed for estimation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61203304,61203055 and 10901145the Fundamental Research Funds for the Central Universities under Grant Nos.2011QNA26,2010LKSX04,and 2010LKSX01
文摘This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors. The two networks can be undirected or directed, and they may also contain isolated nodes and clusters. By using suitable controllers, sufficient conditions for finite-time generalized outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the synchronization time is also numerically demonstrated.
基金supported by the National Natural Science Foundation of China (Grant No. 10901145)
文摘This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochastic differential equations, sufficient conditions for the stability of the error dynamics are derived. Numerical simulations are also shown to demonstrate the effectiveness of these theoretic results.
基金supported by the National Natural Science Foundation of China (Grant No. 10771088)Natural Science Foundation of Jiangsu Province,China (Grant No. 2007098)+3 种基金Outstanding Personnel Program in Six Fields of Jiangsu Province,China (Grant No. 6-A-029)National Natural Science (Youth) Foundation of China (Grant No. 10801140)Youth Foundation of Chongqing Normal University,China (Grant No. 08XLQ04)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 09B 202Z)
文摘This paper introduces a new three dimensional autonomous system with five equilibrium points. It demonstrates complex chaotic behaviours within a wide range of parameters, which are described by phase portraits, Lyapunov exponents, frequency spectrum, etc. Analysis of the bifurcation and Poincar@ map is used to reveal mechanisms of generating these complicated phenomena. The corresponding electronic circuits are designed, exhibiting experimental chaotic attractors in accord with numerical simulations. Since frequency spectrum analysis shows a broad frequency bandwidth, this system has perspective of potential applications in such engineering fields as secure communication.
基金Supported by the National Natural Science Foundation of China under Grant No 10771088, the Natural Science Foundation of Jiangsu under Grant No 2007098, and Outstanding Personnel Program in Six Fields of Jiangsu under Grant No 6-A-029, and the National Natural Science （Youth） Foundation of China under Grant No 10801140, and Youth Foundation of Chongqing Normal University under Grant No 08XLQ04, and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No 09B-202Z.
文摘The new autonomous system with only three equilibrium points is introduced. This system does not belong to the generalized Lorenz systems. The novel attractors are observed over a large range of parameters, which have rarely been reported in previous work. As an important component in chaotic signal generators, a physical circuit has been designed. The experimental results are in agreement with numerical simulations. More significantly, spectral analysis shows that the system has an extremely broad frequency spectral bandwidth in 0-131.6 Hz, without investigating any possible electronic techniques, which is more desirable for secure communications.
基金the National Natural Science Foundation of China (70271065)
文摘It was theoretically proved that one-dimensional transiently chaotic neural networks have chaotic structure in sense of Li-Yorke theorem with some given assumptions using that no division implies chaos. In particular, it is further derived sufficient conditions for the existence of chaos in sense of Li- Yorke theorem in chaotic neural network, which leads to the fact that Aihara has demonstrated by numerical method. Finally, an example and numerical simulation are shown to illustrate and reinforce the previous theory.
基金the National Natural Science Foundation of China(Grant No 10201008).
文摘In the present paper, the fractal rough surface is described by a band-limited Weierstrass-Mandelbrot function. By using the Monte Carlo method and optimal method, a minimal target function method is applied to inverting the fractal dimension of the fractal rough surface. Numerical simulations show that the method can avoid the influence of the fractal characteristic scale, and that the method is of high precision.
