Neural Network based Modeling, Characterization and Identification of Chaotic Systems in Nature

[1]  Sami K. Solanki,et al.  Sunspots: An overview , 2003 .

[2]  Ping Chen,et al.  Study of chaotic dynamical systems via time-frequency analysis , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[3]  Nando de Freitas,et al.  Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks , 2000, UAI.

[4]  B. Shanker,et al.  Convection due to oblique magnetic field in the penumbral region of sunspot , 2006 .

[5]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[6]  Takashi Matsumoto,et al.  A chaotic attractor from Chua's circuit , 1984 .

[7]  R. Washington.  Quantifying chaos in the atmosphere , 2000 .

[8]  Peter Trebatický.  Recurrent Neural Network Training with the Extended Kalman Filter , 2005 .

[9]  Carsten Peterson,et al.  Finding the Embedding Dimension and Variable Dependencies in Time Series , 1994, Neural Computation.

[10]  Recycling Fourier Spectra of Chaotic Systems , 2007 .

[11]  A new algorithm to compute forward and inverse 2-D UMRT for N — A power of 2 , 2012, 2012 International Conference on Power, Signals, Controls and Computation.

[12]  Lee A. Feldkamp,et al.  Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks , 1994, IEEE Trans. Neural Networks.

[13]  Lixing Zhou,et al.  Applications of chaos theory on Partial Discharge detection and character analysis , 2008, 2008 IEEE International Conference on Industrial Technology.

[14]  M. Rosenstein,et al.  A practical method for calculating largest Lyapunov exponents from small data sets , 1993 .

[15]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[16]  L. Cao.  Practical method for determining the minimum embedding dimension of a scalar time series , 1997 .

[17]  Maciej Ogorzalek,et al.  Identification of chaotic systems based on adaptive synchronization , 1997 .

[18]  J. Sprott.  Strange Attractors: Creating Patterns in Chaos , 1993 .

[19]  Floris Takens,et al.  On the numerical determination of the dimension of an attractor , 1985 .

[20]  Steven H. Isabelle,et al.  A signal processing framework for the analysis and application of chaotic systems , 1995 .

[21]  Hong-Guang Ma,et al.  Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction , 2006 .

[22]  Guanrong Chen,et al.  On a new hyperchaotic system , 2008 .

[23]  R.G. Hutchins.  Neural network chaotic system identification , 1996, Conference Record of The Thirtieth Asilomar Conference on Signals, Systems and Computers.

[24]  Sankaran Mahadevan,et al.  Wavelet spectrum analysis approach to model validation of dynamic systems , 2011 .

[25]  I. Daubechies.  Ten Lectures on Wavelets , 1992 .

[26]  Yaakov Bar-Shalom,et al.  Estimation and Tracking: Principles, Techniques, and Software , 1993 .

[27]  Jiaxing Cheng,et al.  A Novel Linear Feedback Control Approach of Lorenz Chaotic System , 2006, CIMCA/IAWTIC.

[28]  J. D. Farmer,et al.  State space reconstruction in the presence of noise" Physica D , 1991 .

[29]  Daniel Stoffer,et al.  Chaotic Behaviour in Simple Dynamical Systems , 1990, SIAM Rev..

[30]  Parameter identification and self-adaptive synchronization of an uncertain time-delayed chaotic system , 2009, 2009 ISECS International Colloquium on Computing, Communication, Control, and Management.

[31]  L. V. Vela-Arevalo.  Time-frequency analysis based on wavelets for Hamiltonian systems , 2002 .

[32]  Frank C. Hoppensteadt,et al.  Analysis and simulation of chaotic systems , 1992 .

[33]  R. Gopikakumari,et al.  A new transform for 2-D signal representation (MRT) and some of its properties , 2004, 2004 International Conference on Signal Processing and Communications, 2004. SPCOM '04..

[35]  Eric Campos-Cantón,et al.  Wavelet analysis of chaotic time series , 2006 .

[36]  James C. Robinson.  Takens ’ embedding theorem for infinite-dimensional dynamical systems , 2005 .

[37]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[38]  R Dr.Gopikakumari,et al.  Development of a New Transform:MRT , 2009 .

[39]  D. Hathaway,et al.  A Standard Law for the Equatorward Drift of the Sunspot Zones , 2011, 1108.1722.

[40]  Carles Simó,et al.  Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing , 2002 .

[41]  Leandro dos Santos Coelho,et al.  Fuzzy Model and Particle Swarm Optimization for Nonlinear Identification of a Chua's Oscillator , 2007, 2007 IEEE International Fuzzy Systems Conference.

[42]  Huang Anshan.  Period doubling and period plus one law-chaotic phenomena in similar Chua's circuit , 1991, China., 1991 International Conference on Circuits and Systems.

[43]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[44]  J. Hurrell,et al.  The North Atlantic Oscillation , 2001, Science.

[45]  Junguo Lu.  Chaotic dynamics of the fractional-order Lü system and its synchronization , 2006 .

[46]  Ramazan Gençay,et al.  Testing chaotic dynamics via Lyapunov exponents , 1998 .

[47]  Bernd Krauskopf,et al.  Global bifurcations of the Lorenz manifold , 2006 .

[48]  M. Ausloos,et al.  SCALING ANALYSIS AND EVOLUTION EQUATION OF THE NORTH ATLANTIC OSCILLATION INDEX FLUCTUATIONS , 2004 .

[49]  Charles Leave.  Neural Networks: Algorithms, Applications and Programming Techniques , 1992 .

[50]  H. Jia,et al.  A New Hyper-Chaotic Lü Attractor and Its Local Bifurcation Analysis , 2009, 2009 International Workshop on Chaos-Fractals Theories and Applications.

[51]  Dongfeng Wang,et al.  A Multi-objective Genetic Programming/ NARMAX Approach to Chaotic Systems Identification , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[52]  O. Rössler.  An equation for continuous chaos , 1976 .

[53]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[54]  L. Palma.  Application of an Extended Kalman Filter for On-line Identification with Recurrent Neural Networks , 2001 .

[55]  Richard J. Greatbatch,et al.  The North Atlantic Oscillation , 2000 .

[56]  A. Rucklidge,et al.  The abrupt development of penumbrae in sunspots , 1995 .

[57]  N. Christophersen,et al.  Chaotic time series : Part 1: estimation of some invariant properties in state space , 1994 .

[58]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[59]  Mahesan Niranjan,et al.  The EM algorithm and neural networks for nonlinear state space estimation , 1998 .

[60]  Simulation and analysis of Lorenz system's dynamics characteristics , 2009, 2009 International Conference on Image Analysis and Signal Processing.

[61]  Sy-Miin Chow,et al.  An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models , 2007, Multivariate behavioral research.

[62]  Clyde Meador.  Numerical Calculation of Lyapunov Exponents for Three-Dimensional Systems of Ordinary Differential Equations , 2011 .

[63]  Sarita Azad,et al.  Wavelets Detecting Chaos in logistic Map , 2003 .

[64]  H. Leung,et al.  An EM based method for semi blind identification of linear systems driven by chaotic signals , 2004, IEEE Conference on Cybernetics and Intelligent Systems, 2004..

[65]  M. Ataei,et al.  Estimating the Lyapunov exponents of chaotic time series: A model based method , 2003, 2003 European Control Conference (ECC).

[66]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[67]  A. Willsky,et al.  Signals and Systems , 2004 .

[68]  L. Chua.  Dynamic nonlinear networks: State-of-the-art , 1980 .

[69]  G..  A Theory for Multiresolution Signal Decomposition : The Wavelet Representation , 2004 .

[70]  L. Chua,et al.  A universal circuit for studying and generating chaos. II. Strange attractors , 1993 .

[71]  E. Gerber.  A dynamical and statistical understanding of the North Atlantic Oscillation and annular modes , 2005 .

[72]  Guanrong Chen,et al.  Local bifurcations of the Chen System , 2002, Int. J. Bifurc. Chaos.

[73]  Mit Press,et al.  Fast Fourier Transform Hardware Implementations—An Overview , 1969 .

[74]  Henry Leung,et al.  Blind identification of autoregressive system using chaos , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[75]  Péter Torma.  Combining Local Search, Neural Networks and Particle Filters to Achieve Fast and Reliable Contour Tracking , 2002 .

[76]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[77]  K. Ramasubramanian,et al.  A comparative study of computation of Lyapunov spectra with different algorithms , 1999, chao-dyn/9909029.

[78]  Daniel S. Yeung,et al.  Prediction of chaotic time series using L-GEM based RBFNN , 2009, 2009 International Conference on Machine Learning and Cybernetics.

[79]  R Gopikakumari,et al.  Investigations On The Development Of An Ann Model & Visual Manipulation Approach For 2-D Dft Computation In Image Processing , 1998 .

[80]  Ercan Solak,et al.  Partial identification of Lorenz system and its application to key space reduction of chaotic cryptosystems , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[81]  Scott M. Osprey,et al.  Evidence for the chaotic origin of Northern Annular Mode variability , 2011 .

[82]  J. L. Roux.  An Introduction to the Kalman Filter , 2003 .

[83]  Huang Qi,et al.  Chaos system filter on state-space model and EKF , 2009, 2009 IEEE International Conference on Automation and Logistics.

[84]  A. Doucet,et al.  A Tutorial on Particle Filtering and Smoothing: Fifteen years later , 2008 .

[85]  Thomas B. Schön,et al.  Marginalized particle filters for mixed linear/nonlinear state-space models , 2005, IEEE Transactions on Signal Processing.

[86]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[87]  S. Grillo,et al.  Bifurcation analysis and Chaos detection in power systems , 2008, 2008 43rd International Universities Power Engineering Conference.

[88]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[89]  C. Chandré,et al.  Instantaneous frequencies of a chaotic system , 2005 .