Symbolic Vector Dynamics Approach to Initial Condition and Control Parameters Estimation of Coupled Map Lattices

In this paper, we extend symbolic dynamics, a standard analytical method for 1-D chaotic map, and initiate a solution to the problem of estimation in coupled map lattices (CMLs) by introducing the symbolic vector dynamics. We develop a novel technique for estimating initial conditions. We also expand the applicable scope of a word-lifting technique for parameter estimation from a 1-D chaotic map to CMLs. Both theoretical and experimental results show that those algorithms can construct one-to-one correspondence between the set of global orbits and the set of admissible codes. Therefore, we provide novel analytical techniques for understanding turbulences in CMLs.

[1]  Zeng Yi-Cheng,et al.  A statistical property to recover coarsely initial conditions from coupled map lattices , 2005 .

[2]  Xiaogang Wu,et al.  Parameter estimation only from the symbolic sequences generated by chaos system , 2004 .

[3]  Ling Cong,et al.  A general efficient method for chaotic signal estimation , 1999 .

[4]  ZengYi-Cheng,et al.  A statistical property to recover coarsely initial conditions from coupled map lattices , 2003 .

[5]  Henry Leung,et al.  An ergodic approach for chaotic signal estimation at low SNR with application to ultra-wide-band communication , 2006, IEEE Transactions on Signal Processing.

[6]  Gang Hu,et al.  PSEUDO-RANDOM NUMBER GENERATOR BASED ON COUPLED MAP LATTICES , 2004 .

[7]  Wolfram Just,et al.  Analytical Approach for Piecewise Linear Coupled Map Lattices , 1997, chao-dyn/9711014.

[8]  Gang Hu,et al.  Chaos-based secure communications in a large community. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  R. Coutinho,et al.  Extended symbolic dynamics in bistable CML: existence and stability of fronts , 1997 .

[10]  E. Bollt,et al.  Symbolic dynamics of coupled map lattices. , 2006, Physical review letters.

[11]  Liu Ying,et al.  Recovery of statistical property of initial conditions based on time-varying parameter from coupled map lattices , 2006 .

[12]  G. Álvarez,et al.  Cryptanalysis of an ergodic chaotic cipher , 2003 .

[13]  Roy Tenny,et al.  Additive mixing modulation for public key encryption based on distributed dynamics , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Wenjiang Pei,et al.  Estimating initial conditions in coupled map lattices from noisy time series using symbolic vector dynamics , 2007 .

[15]  Wolfram Just,et al.  Non-Equilibrium Behaviour in Unidirectionally Coupled Map Lattices , 2001 .

[16]  Haralabos C. Papadopoulos,et al.  Maximum-likelihood estimation of a class of chaotic signals , 1995, IEEE Trans. Inf. Theory.

[17]  Roy Tenny,et al.  Using distributed nonlinear dynamics for public key encryption. , 2003, Physical review letters.

[18]  Ljupco Kocarev,et al.  Applications of symbolic dynamics in chaos synchronization , 1997 .

[19]  Venkatesh Nagesha,et al.  Methods for chaotic signal estimation , 1995, IEEE Trans. Signal Process..

[20]  T. Schimming,et al.  Symbolic dynamics for processing chaotic signals. I. Noise reduction of chaotic sequences , 2001 .

[21]  Pei Wen-Jiang,et al.  Initial condition estimation from coupled map lattices based on symbolic vector dynamics , 2007 .

[22]  Bailin Hao.  Applied Symbolic Dynamics , 1998 .

[23]  Steven Kay,et al.  Asymptotic maximum likelihood estimator performance for chaotic signals in noise , 1995, IEEE Trans. Signal Process..

[24]  Henry Leung,et al.  Estimating initial conditions of noisy chaotic signals generated by piecewise linear Markov maps using itineraries , 1999, IEEE Trans. Signal Process..

[25]  Guanrong Chen,et al.  A multiple pseudorandom-bit generator based on a spatiotemporal chaotic map , 2006 .

[26]  T. Schimming,et al.  Symbolic dynamics for processing chaotic signals Part II : communication and coding , 2001 .