Fisher information and nonlinear dynamics

The past decade has witnessed an impressive growth in the scope and variety of physical applications of Fisher's information measure (FIM). As a consequence, FIM is widely regarded today as providing one with a unifying principle for physics. In the present paper, we investigate its usefulness in connection with the description of important aspects of the behavior of dynamical systems, and find that the unification referred to above can be extended to the field of these systems.

[1]  Plastino.  Symmetries of the Fokker-Planck equation and the Fisher-Frieden arrow of time. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  A. R. Plastino,et al.  Tsallis-like information measures and the analysis of complex signals , 2000 .

[3]  N. Packard,et al.  Power spectral analysis of a dynamical system , 1980 .

[4]  L. G. Gamero,et al.  Wavelet analysis and nonlinear dynamics in a nonextensive setting , 1997 .

[5]  J. D. Farmer,et al.  ON DETERMINING THE DIMENSION OF CHAOTIC FLOWS , 1981 .

[6]  B. Frieden,et al.  Lagrangians of physics and the game of Fisher-information transfer. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Robert C. Hilborn,et al.  Chaos and Nonlinear Dynamics , 2000 .

[8]  A lower bound for Fisher's information measure , 1996 .

[9]  E. A. Jackson,et al.  Perspectives of nonlinear dynamics , 1990 .

[10]  Michael C. Mackey,et al.  Chaos, Fractals, and Noise , 1994 .

[11]  DECREASE OF THE FISHER INFORMATION FOR SOLUTIONS OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION WITH MAXWELLIAN MOLECULES , 2000 .

[12]  B. Frieden.  Physics from Fisher information , 1998 .

[13]  A. Plastino,et al.  Fisher's information, Kullback's measure, and H-theorems , 1998 .

[14]  O. Rössler.  CONTINUOUS CHAOS—FOUR PROTOTYPE EQUATIONS , 1979 .

[15]  C. Beck,et al.  Thermodynamics of chaotic systems , 1993 .

[16]  B H Soffer,et al.  Fisher-based thermodynamics: its Legendre transform and concavity properties. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Knut H. Alfsen,et al.  Lyapunov-exponent spectra for the Lorenz model , 1984 .