复杂系统混沌行为判别与混沌时间序列的分形建模

Chaotic Behavior Decision of Complex System and Fractal Based Chaotic Time Serials Modeling

提出了以有限维自由度及Lyapunov指数联合分析为判据的复杂系统混沌行为判别方法．避免了判别过程中将纯随机行为及复杂确定性线性行为误判为混沌行为。以球磨机矿浆流量为例,在相空间重构的基础上对系统关联维数进行了分析．验证了系统具有有限维自由度。通过Lyapunov指数分析考察了系统的时空演化特性并验证了系统的初值敏感性,从而分析出该流量具有确定性与随机性相互统一的混沌运动特征。利用Hurst指数通过分形内插算法对流量信号进行了精确重构,建立了一种可准确重演系统时空变化规律的模型．

A combination analysis approach composed of finite degree of freedom and Lyapunov exponent is presented for determining the chaotic behavior of a complex system. The approach avoids the common problems of error estimation in the pure stochastic systems and complex deterministic non-linear systems to chaotic systems. The mine plasma traffic is used as an analysis object, the phase space of the traffic time serials is reconstructed and the correlation dimension is analyzed, which indicate that the dynamical system has finite degree of freedom. The nonlinear evolution mechanism is observed and the initial value sensitive characteristic of the system is demonstrated through Lyapunov exponent analysis. Finally, the traffic serials signalsare reconstructed by using fractal interpolation algorithm and gaining reasonably accurate models.