Physics
Scientific paper
Jun 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000aipc..519..365k&link_type=abstract
STATISTICAL PHYSICS: Third Tohwa University International Conference. AIP Conference Proceedings, Volume 519, pp. 365-367 (2000
Physics
Self-Organized Systems, Low-Dimensional Chaos, Stochastic Analysis Methods
Scientific paper
We derive an approximation formula for obtaining parameter dependence of statistical quantities in chaotic systems on the basis of a Frobenius-Perron equation. The formula is characterized by three integers; One is the number of application of the Frobenius-Perron operator, the second is the number of the delta-peaks of the initial density, and the third is the number of the integration domains. We find numerically that this formula is applicable to a wide variety of states of a system ranging from stable cycles to band-chaos and totaly spread chaotic regime by merely changing the system parameter, except for the very narrow windows representing stable cycles with large periodicity, where the concrete examples are a logistic map, a Hénon map and so on. We finally consider how we extend our theory to ODE's. .
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