PMID: 11308747Apr 20, 2001Paper

Lyapunov exponents in disordered chaotic systems: avoided crossing and level statistics

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
V AhlersArkady S. Pikovsky

Abstract

The behavior of the Lyapunov exponents (LEs) of a disordered system consisting of mutually coupled chaotic maps with different parameters is studied. The LEs are demonstrated to exhibit avoided crossing and level repulsion, qualitatively similar to the behavior of energy levels in quantum chaos. Recent results for the coupling dependence of the LEs of two coupled chaotic systems are used to explain the phenomenon and to derive an approximate expression for the distribution functions of LE spacings. The depletion of the level spacing distribution is shown to be exponentially strong at small values. The results are interpreted in terms of the random matrix theory.

References

Mar 28, 1994·Physical Review Letters·R Roy, K S Thornburg
Oct 25, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·R ZillmerA Pikovsky

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Citations

Sep 8, 2010·The Review of Scientific Instruments·P UrbanA Srnka
Apr 5, 2011·Chaos·M WolfrumY L Maistrenko
Jun 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Nirmal PunethaRam Ramaswamy
Aug 12, 2009·Journal of Developmental and Behavioral Pediatrics : JDBP·Paul BangiranaMichael J Boivin
Sep 12, 2007·Cognitive and Behavioral Neurology : Official Journal of the Society for Behavioral and Cognitive Neurology·Sandy A NeargarderKaren D Sullivan
Dec 15, 2006·Journal of Learning Disabilities·Benjamin J Lovett, Lawrence J Lewandowski
Dec 4, 2012·Neurosurgical Focus·Louis De BeaumontNadia Gosselin
Apr 15, 2016·Physical Review. E·Soumen K Patra, Anandamohan Ghosh
Mar 20, 2018·Physical Review. E·Masanori HanadaMasaki Tezuka
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Rajat KarnatakRam Ramaswamy
Jun 13, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tooru Taniguchi, Gary P Morriss
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ivan G SzendroMiguel A Rodríguez

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