动态系统-国立交通大学应用数学系.pptVIP

Properties of MLM Chaotic map No windows Uniform distribution Equivalent Pseudorandom MLM: chaotic map MLM: no windows MLM: no windows MLM: uniform distribution (FFT) r = 5.9 MLM: equivalent (bits error rate analysis) MLM: equivalent (Poincaré recurrence) MLM: pseudorandom (SP 800-22) 3 2D charged particles 3 2D charged particles 3 2D charged particles 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. 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. References 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. List of chaotic maps. /wiki/List_of_chaotic_maps 動態系統, 動力系統, 混沌理論. /zh-tw/ References Thank you for your attention! Devanveys chaos 傳遞性(transitivity)： 可到處遍歷。 Random vs. Chaos Identity： 1. Continuous Spectrum 2. Correlation Function： Random numbers: Chaotic signals: Random vs. Chaos Observable: Temporal Average for (1): Perturbation: Temporal Average for (2): 3. Stability： Random vs. Chaos Distinction： MLM: pseudorandom 連續動態系統: Duffing equation 連續動態系統: Van der Pol oscillator 連續動態系統: R?ssler system 連續動態系統: Lorenz system 動態系統模型: modified logistic map 動態系統模型: 3 2D charged particles 動態系統模型: 3 vortices system Q1. Observe the behavior of the map 3n +1. Q2. Observe the behavior of tent map with μ = 2. Q3. Observe the behavior of logist