Statistics – Computation
Scientific paper
Aug 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987stin...8813207o&link_type=abstract
Unknown
Statistics
Computation
Behavior, Chaos, Nonlinear Systems, Tracking (Position), Trajectories, Hyperspaces, Maps, Mathematical Models, Phase-Space Integral, Polynomials, Stability
Scientific paper
A theoretical conjecture is made about the nature of chaotic behavior in systems with simple maps. This conjecture gives rise to a computational scheme based on trajectories starting from the maximum in the system map. These trajectories are called supertracks and their loci in the parameter phase-space indexed by iteration number are called supertracks functions. The chaotic regimes of two nonlinear systems with a single maximum are studied using this scheme. It is found that the behavior in these regimes can be characterized recursively by supertrack functions. At low recursion order these functions analytically describe the gross features of the chaotic regime (i.e. bounding envelopes, stable cycles, star points, etc.). They can be iterated to higher orders to study higher order features. The methodology employed is general enough to be used to study other nonlinear systems. It also has potential for identifying chaotic behavior experimentally. Universality is the basis for theoretically understanding the results.
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