An efficient QR based method for the computation of Lyapunov exponents

Abstract An efficient and numerically stable method to determine all the Lyapunov characteristic exponents of a dynamical system is developed. Numerical experiments are presented highlighting some aspects of convergence, accuracy and efficiency in the computation of the Lyapunov characteristic exponents.

[1]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[2]  Ulrich Parlitz,et al.  Comparison of Different Methods for Computing Lyapunov Exponents , 1990 .

[3]  L. Dieci,et al.  Computation of a few Lyapunov exponents for continuous and discrete dynamical systems , 1995 .

[4]  G. Benettin,et al.  Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory , 1980 .

[5]  I. Tsuda,et al.  A new method for computing Lyapunov exponents , 1993 .

[6]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

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

[8]  Peter Läuchli,et al.  Jordan-Elimination und Ausgleichung nach kleinsten Quadraten , 1961 .

[9]  Åke Björck,et al.  Numerical Methods , 2021, Markov Renewal and Piecewise Deterministic Processes.

[10]  Gene H. Golub,et al.  Matrix computations , 1983 .

[11]  A. Booth.  Numerical Methods , 1957, Nature.

[12]  I. Shimada,et al.  A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems , 1979 .

[13]  G. Benettin,et al.  Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application , 1980 .

[14]  Å. Björck.  Numerics of Gram-Schmidt orthogonalization , 1994 .

[15]  B. Parlett.  The Algebraic Eigenvalue Problem (J. H. Wilkinson) , 1966 .