基于系统Lyapunov指数分析的倍周期分岔研究

Study on period doubling bifurcation based on systematic Lyapunov exponent analysis

作为动力系统的一个重要特征值 ,L yapunov指数表征系统轨道的收敛或发散程度。首先对渐近稳态系统的 L yapunov指数进行重新定义 ;然后利用系统的稳定性条件及分岔条件 ,对系统倍周期分岔点微小邻域内 L yapunov指数的变化趋势进行推导 ;

As an important characteristic variable of dynamical system, Lyapunov exponent indicates the convergentordivergentdegreeofsystem orbits. Lyapunov exponent is redefined in asymptotically stable system, and based on it, the changing tendency of Lyapunov exponent in little neighborhood of period doubling bifurcationpointsisderivedbymeansofsystem stability condition and period doubling bifurcation condition. The theoretically derived results are utilized to analyze some attribute and behavior of a kind of dynamical economy model.