科学计算之动态系统介绍.ppt

Poincaré map Lyapunov exponent Lyapunov exponent [ Definition] global Lyapunov exponent [Computation] local Lyapunov exponent (average the phase-space volume expansion along trajectory) Local Lyapunov exponent Local Lyapunov exponent Poincaré recurrence positive topological entropy Homoclinic orbit MLM: modified logistic map Logistic map Modified Logistic map Properties of MLM Chaotic map No windows Uniform distribution Equivalent Pseudorandom MLM: chaotic map MLM: no windows MLM: no windows MLM: Poincaré recurrence MLM: uniform distribution (FFT) r = 5.9 MLM: equivalent (bits error rate analysis) MLM: pseudorandom MLM: pseudorandom (SP 800-22) V. Afraimovich, J. Schmeling, E. Ugalde, J. Urias, Spectra of dimensions for Poincare recurrences, Discrete Contin. Dyn. Syst. 6 (4) (2000) 901-914. S. M. Chang, M. C. Li and W. W. Lin, Asymptotic synchronization of modified logistic hyper-chaotic systems and its applications. Nonlinear Analysis: Real World Applications, Vol. 10, Issue 2 (2009), pp. 869–880. S. M. Chang, T. C. Lin and W. W. Lin, Chaotic and Quasiperiodic Motions of Three Planar Charged Particles. Int. J. Bifurcation Chaos, Vol. 11, No. 7 (2001), pp. 1937–1951. References S. M. Chang, T. C. Lin and W. W. Lin, Dynamics of Vortices in Two-Dimensional Bose-Einstein Condensates. Int. J. Bifurcation Chaos, Vol. 12, No. 4 (2002), pp. 739–764. S. L. Chen, S. M. Chang, T. T. Hwang and W. W. Lin, Digital secure-communication using robust hyper-chaotic systems. Int. J. Bifurcation Chaos, Vol. 18, No. 11 (2008), pp. 1–14. T. S. Parker L. O. Chua, Practical Numerical Algorithm for Chaotic Systems, Ch.3, Springer-Verlag, 1989. B. Saussol, S. Troubetzkoy, S. Vaienti, Recurrence, dimensions and Lyapunov exponents, J. Statist. Phys. 106 (314) (2002) 623–634. References List of chaotic maps. /wiki/List_of_chaotic_maps 動態系統, 動力系統, 混沌理論. /zh-tw/ Lyapunov Exponents, Chaos and Time-Series Analysis. /phys505/lect05.htm References Thank you