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Mappings - Small Perturbations to Control Chaos

hys. Rev. A, 1988; 37:1711-172418AuerbachD, CvitanovicPandEckmannJP, eta1. Ex-ploringchaoticmotionthroughperiodicorbits. Phys. Rew. Lett. . 1987; 58:2387-238919ZhangWen. ZhangHuishengandXuXiaofeng. Studyofgeneralnonlinearformulaofoil-filmforceactingonajournalwithunsteadymotion. Asia-PacificVibrationConfeFences. Korea. 1997218 Vibration Engineering Volume 16 2O YU Jie. MDOF rotor system Numerical analysis of nonlinear dynamics and chaos control. [PhD thesis]. Dalian: Dalian University of Technology Department of Engineering Mechanics, 200,221 Lu and Xiang,[link widoczny dla zalogowanych], YU Jie,[link widoczny dla zalogowanych], Qiu Spring Air. Precise integration of the nonlinear dynamic integral equations and its solution. Solid Mechanics, 2001; 22 (3): 3O3-3O822 Hao Bolin, ZHANG Shu Yu. Of forced nonlinear oscillator in the period doubling bifurcation and chaos phenomena of frequency sampling method. Physics, 1983; 32 (2) :198 - 208ChaosControlBasedonContractionMappingsandSmallPerturbationsYuHongieIHexiang (DepartmentofEngineeringMechanics.DalianUniversityofTechnologyDalian, 116023) AbstractAmethodusingcompactmapping-smallparameterperturbationtocontrolthechaoticbehaviorispresented. Bymeansofthetemporalsmallperturbationfeedbackoftheadjustableparametersofthesystem, oneoftheinfinitenumberoftheunstableperiodicorbitsembeddedinthechaoticattractorisdirectedandisstabilizedontothedesiredorbit. ThemethodisusedtocontrolthechaoticmotionsofnonlinearrotorsystemandDullingsystem. Numericalresultsshowthatthemethodiseffective. Keywords: nonlinearvibratoin; ceriodicorbit; chaos; control; contractionmappings the first of the cleaning woman, Yu Hong, Ph.D., 1968. Tel: 13645602600, E-mail: y-yh! I @ sina. corn magazine 16 2003 1 12 Formula (12) read as follows: M2Q + (K2 one. M2) Q + H. Weiwei Gu Ji c, + F-1. Dh * ...) OQ,[link widoczny dla zalogowanych], Q + a + n. b} Q +1 A (4E + E2k + E. 3k,)] qQ, a Σ + one by one [2. +. RsinO + O (u. + RcosO)] G2 a 1,[link widoczny dla zalogowanych],2 a Ⅳ 2k , ...,[link widoczny dla zalogowanych], n2 (12) / [Σ Bu ¨ FΣ vii ΣΣ + QQ},, C a ¨ C, 2ΣΣQQQQQQ, from a uDΣΣΣ Pu Q gl II MΣ2

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