Universal bifurcation property of two- or higher-dimensional dissipative systems in parameter space: why does 1D symbolic dynamics work so well?

The universal bifurcation property of the Henon map in parameter space is studied with symbolic dynamics. The universal-L region is defined to characterize the bifurcation universality. It is found that the universal-L region for relatively small L, is not restricted to very small b values. These results show that the fact that universal sequences with short period can be found in many nonlinear dissipative systems is also a universal phenomenon.

[1]  J. Gallas,et al.  Structure of the parameter space of the Hénon map. , 1993, Physical review letters.

[2]  Brun,et al.  Model identification by periodic-orbit analysis for NMR-laser chaos. , 1991, Physical review letters.

[3]  Cvitanovic,et al.  Topological and metric properties of Hénon-type strange attractors. , 1988, Physical review. A, General physics.

[4]  Mogens H. Jensen,et al.  Universal strange attractors on wrinkled tori , 1988 .

[5]  Parisi,et al.  Topological and metric analysis of heteroclinic crisis in laser chaos. , 1992, Physical review letters.

[6]  Nicholas C. Metropolis,et al.  On Finite Limit Sets for Transformations on the Unit Interval , 1973, J. Comb. Theory A.

[7]  M. Hénon,et al.  A two-dimensional mapping with a strange attractor , 1976 .

[8]  D. R. Moore,et al.  Dynamics of double convection , 1990, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[9]  McCormick,et al.  Multiplicity in a chemical reaction with one-dimensional dynamics. , 1986, Physical review letters.

[10]  A. Wolf,et al.  One-Dimensional Dynamics in a Multicomponent Chemical Reaction , 1982 .

[11]  R. Ball,et al.  The interpretation and measurement of the f(α) spectrum of a multifractal measure , 1990 .

[12]  B. Hao,et al.  Elementary Symbolic Dynamics And Chaos In Dissipative Systems , 1989 .

[13]  Bai-lin HAO,et al.  SYMBOLIC DYNAMICS AND SYSTEMATICS OF PERIODIC WINDOWS , 1986 .

[14]  M. Proctor,et al.  Normal forms and chaos in thermosolutal convection , 1990 .

[15]  S. A. Wouthuysen.  On the excitation mechanism of the 21 cm interstellar hydrogen emission line , 1952 .

[16]  Dynamics of strongly dissipative systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  H. Fang,et al.  Symbolic dynamics of the Lorenz equations , 1996 .

[18]  Antonio Politi,et al.  On the topology of the Hénon map , 1990 .

[19]  Gunaratne,et al.  Chaos beyond onset: A comparison of theory and experiment. , 1989, Physical review letters.

[20]  Stéphan Fauve,et al.  Two-parameter study of the routes to chaos , 1983 .

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

[22]  P. Grassberger,et al.  Generating partitions for the dissipative Hénon map , 1985 .