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中国物理学会期刊

强迫布鲁塞尔振子奇异吸引子的柯尔莫哥洛夫容量和李雅普诺夫维数

CSTR: 32037.14.aps.33.1246

KOLMOGOROV CAPACITY AND LYAPUNOV DIMENSION OF STRANGE ATTRACTORS OF FORCED BRUSSELATOR

CSTR: 32037.14.aps.33.1246
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  • 本文用周期采样降低吸引子维数的办法,计算和讨论了强迫布鲁塞尔振子的几种典型吸引子的柯尔莫哥洛夫容量dC和李雅普诺夫维数dL。结果表明,人们关于dC和dL关系的推测是正确的。这些推测是:当最大李雅普诺夫指数λ1>0时dC=dL关系成立,当λ1=0时dC=dL关系不一定成立。文中指出和论证了强迫布鲁塞尔振子的Runge-Kutta差分方程使上述算法给出的dC不收敛的原因和克服办法。文中还指出:可能是类似的微分方程的差分化的原因,使得用单个观察量的时间系列来计算容量的办法遇到了发散困难。

     

    In this paper, by using stroboscopic sampling method which reduces the dimension of attractors, the Kolmogorov Capacity dC and Lyapunov dimension dL of some typical attractors of forced Brusselator are computed. The results show that the conjectures of ref. 6, 16 about the relations between dC and dL are correct. We spell out these conjectures as that if the maximal Lyapunov exponent λ1>0, then dC=dL; if λ1=0, then there exist examples that do not satisfy dC=dL. The reasons for noncon-vergence of dC for the forced Brusselator Caculated by using the Runge-Kutta difference equations and the way to improve it are pointed out and tested numerically. We conjecture further that by the same reason of using difference equations to approach differential equations, the capacity caculated from time series of a single observable may not be convergent.

     

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