Stability of Subharmonic Solutions

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1987 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Applied Mathematics, volume 47, pages 244-253 (issn: 0036-1399, eissn: 1095-712X,

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Authors: Chan, Whei-Ching C.;

doi: 10.1137/0147016

Stability of Subharmonic Solutions

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Abstract

Summary: Consider the equation ẍ\(+g(x)=-\lambda \dot x+\mu f(t)\) where x is real, g is smooth, \(f(t+1)=f(t)\) and \(\lambda\) and \(\mu\) are small parameters. By using periodic Mel'nikov functions and the method of Lyapunov-Schmidt, we determine all the Floquet multipliers of the bifurcating subharmonic solutions of order k, \(k=1,2,... \).

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Michigan State University
United States

Keywords

Local and nonlocal bifurcation theory for dynamical systems, Floquet multipliers, bifurcating subharmonic solutions, Lyapunov-Schmidt, Stability theory for smooth dynamical systems, periodic Mel'nikov functions

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