On the computation of characteristic multipliers for predicting limit cycle bifurcations
type: Item
instance of: scholarly article
title: On the computation of characteristic multipliers for predicting limit cycle bifurcations
zbMATH Open document ID: 0940.34023
DOI: 10.1016/S0960-0779(97)00055-6
author: G. Torrini
author: R. Genesio
author: Alberto Tesi
published in: Chaos, Solitons and Fractals
publication date: 2000-01-24T00:00:00Z
review text: The authors consider local bifurcations of limit cycles in nonlinear dynamical systems. They develop a simple technique to estimate the characteristic multipliers of a limit cycle, using a first-order harmonic balance approximation to the periodic solution under study. This technique analyzes the loss of stability of the limit cycle and gives effective conditions for the prediction of the cyclic fold, flip and Neimark-Sacker bifurcation phenomena; in particular efficient results are given for third-order systems. Several examples are presented.
reviewed by: Abdelkader Boucherif
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34-04
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 37G15
zbMATH DE Number: 1392785
zbMATH Keywords: characteristic multipliers
zbMATH Keywords: limit cycle
zbMATH Keywords: bifurcation
zbMATH Keywords: harmonic balance method
MaRDI profile type: Publication
cites work: Practical bifurcation and stability analysis: from equilibrium to chaos.
cites work: Q4885523
cites work: Elements of applied bifurcation theory
cites work: A describing-function based criterion for a route to chaos in autonomous nonlinear systems
cites work: NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
cites work: Q3029380
cites work: Q3141919
cites work: The inverse multiple input describing function problem
cites work: Models of complex dynamics in nonlinear systems
cites work: A HARMONIC BALANCE APPROACH FOR CHAOS PREDICTION: CHUA’S CIRCUIT
description: scientific article; zbMATH DE number 1392785