This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different ...This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.展开更多
A complete spectrum of Lyapunov exponents (LEs) is obtained from 1970— 1985 daily mean pressure measurements at Shanghai by means of a correlation matrix analysis technique and it is found that there exist LEs≥0, an...A complete spectrum of Lyapunov exponents (LEs) is obtained from 1970— 1985 daily mean pressure measurements at Shanghai by means of a correlation matrix analysis technique and it is found that there exist LEs≥0, and <0. with their sum <zero (∑λ_1<0), thus showing the evolution of the climate-weather system represented by the series to be chaotic. The sum of positive LE is known to represent the bodily divergence of the system and the sum of these positive LEs is theoretically found to be Kolmogorov entropy of the system. This paper shows that with the time lag τ=5, the parameter m=2 and the dimensionality d_M=9, the sum of the positive LEs sum fromλ_i>0λ_i=K=0.110405 whereupon T=1 /K =9 is obtained as the predictable time scale, a result close to that acquired by the dynamic-statistical approach in early days and also in agreement with that present by the authors themselves(1991).展开更多
文摘This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.
文摘A complete spectrum of Lyapunov exponents (LEs) is obtained from 1970— 1985 daily mean pressure measurements at Shanghai by means of a correlation matrix analysis technique and it is found that there exist LEs≥0, and <0. with their sum <zero (∑λ_1<0), thus showing the evolution of the climate-weather system represented by the series to be chaotic. The sum of positive LE is known to represent the bodily divergence of the system and the sum of these positive LEs is theoretically found to be Kolmogorov entropy of the system. This paper shows that with the time lag τ=5, the parameter m=2 and the dimensionality d_M=9, the sum of the positive LEs sum fromλ_i>0λ_i=K=0.110405 whereupon T=1 /K =9 is obtained as the predictable time scale, a result close to that acquired by the dynamic-statistical approach in early days and also in agreement with that present by the authors themselves(1991).
