Bifurcation and chaos in escape equation model by incremental harmonic balancing
type: Item
instance of: scholarly article
title: Bifurcation and chaos in escape equation model by incremental harmonic balancing
zbMATH Open document ID: 0962.70023
DOI: 10.1016/S0960-0779(99)00044-2
author: N. Delaunay
published in: Chaos, Solitons and Fractals
publication date: 2000-08-09T00:00:00Z
review text: Periodic motions of the nonlinear system representing the escape equation with cosine and sine parametric excitations and external harmonic excitations are obtained by the incremental harmonic balance (IHB) method. The system contains quadratic stiffness terms. The authors derive explicitly the Jacobian matrix and residue vector for the nonlinearity due to parametric excitation. An arc length path following procedure is used in combination with Floquet theory to trace the response diagram and to investigate the stability of periodic solutions. The system undergoes chaotic motions for increase in the amplitude of harmonic excitation, which is investigated by numerical integration and represented in terms of phase plane, Poincaré sections and Lyapunov exponents. The authors use interpolated cell mapping method to obtain the initial condition map corresponding to two coexisting period 1 motions. The periodic motions and bifurcation points obtained by the IHB method compare very well with results of numerical integration.
reviewed by: Fuhua Ling
Mathematics Subject Classification ID: 70K50
Mathematics Subject Classification ID: 70K55
Mathematics Subject Classification ID: 70K40
zbMATH DE Number: 1486572
zbMATH Keywords: escape equation
zbMATH Keywords: incremental harmonic balance method
zbMATH Keywords: parametric excitations
zbMATH Keywords: Floquet theory
zbMATH Keywords: chaotic motions
zbMATH Keywords: quadratic stiffness terms
zbMATH Keywords: Jacobian matrix
zbMATH Keywords: arc length path following procedure
zbMATH Keywords: stability of periodic solutions
zbMATH Keywords: numerical integration
zbMATH Keywords: phase plane
zbMATH Keywords: Poincaré sections
zbMATH Keywords: Lyapunov exponents
zbMATH Keywords: interpolated cell mapping method
zbMATH Keywords: bifurcation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1486572