In this paper, with the theory of nonlinear dynamic systems, It is analyzed that the dynamic behavior and the predictability for the monthly mean variations of the sunspot relative number recorded from January 1891 to...In this paper, with the theory of nonlinear dynamic systems, It is analyzed that the dynamic behavior and the predictability for the monthly mean variations of the sunspot relative number recorded from January 1891 to December 1996. In the progress, the fractal dimension (D = 3.3 +/- 0.2) for the variation process rt as computed. This helped us to determine the embedded dimension [2 x D + 1] = 7. By computing the Lyapunov index (lambda(1) = 0.863), it was indicated that the variation process is a chaotic system. The Kolmogorov entropy (K = 0.0260) was also computed, which provides, theoretically, the predicable time scale. And at the end, according to the result of the analysis above, an experimental predication is made, whose data was a part cut from the sample data.展开更多
This paper concerns with global bifurcations of limit cycles for a cubic system.The uniqueness of limit cycles is proved in Hopf and Poincare bifurcations.
文摘In this paper, with the theory of nonlinear dynamic systems, It is analyzed that the dynamic behavior and the predictability for the monthly mean variations of the sunspot relative number recorded from January 1891 to December 1996. In the progress, the fractal dimension (D = 3.3 +/- 0.2) for the variation process rt as computed. This helped us to determine the embedded dimension [2 x D + 1] = 7. By computing the Lyapunov index (lambda(1) = 0.863), it was indicated that the variation process is a chaotic system. The Kolmogorov entropy (K = 0.0260) was also computed, which provides, theoretically, the predicable time scale. And at the end, according to the result of the analysis above, an experimental predication is made, whose data was a part cut from the sample data.
文摘This paper concerns with global bifurcations of limit cycles for a cubic system.The uniqueness of limit cycles is proved in Hopf and Poincare bifurcations.
