On the application of the homotopy analysis method to limit cycles' approximation in planar self-excited systems
type: Item
instance of: scholarly article
title: On the application of the homotopy analysis method to limit cycles' approximation in planar self-excited systems
zbMATH Open document ID: 1254.34034
author: Huaxiong Chen
author: Jianhe Shen
author: Zheyan Zhou
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2012-09-13T00:00:00Z
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 6081965
zbMATH Keywords: homotopy analysis method
zbMATH Keywords: planar self-excited system
zbMATH Keywords: strong nonlinearity
zbMATH Keywords: limit cycle
zbMATH Keywords: predator-prey model
MaRDI profile type: Publication
full work available at URL: j.cnsns.2012.03.025
OpenAlex ID: W1963588310
cites work: Q5682682
cites work: Q3895818
cites work: Perturbation methods in applied mathematics
cites work: Q4680537
cites work: A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators
cites work: An elliptic Lindstedt-Poincaré method for certain strongly nonlinear oscillators
cites work: A hyperbolic Lindstedt-Poincaré method for homoclinic motion of a kind of strongly nonlinear autonomous oscillators
cites work: Amplitude Incremental Variational Principle for Nonlinear Vibration of Elastic Systems
cites work: Q4510589
cites work: Purely analytic solutions of magnetohydrodynamic swirling boundary layer flow over a porous rotating disk
cites work: Notes on the homotopy analysis method: some definitions and theorems
cites work: A note on the homotopy analysis method
cites work: On perturbation procedure for limit cycle analysis
cites work: Comparison between the homotopy analysis method and homotopy perturbation method
cites work: Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt
cites work: Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation
cites work: Convergence of the homotopy perturbation method
cites work: Elements of applied bifurcation theory
DOI: 10.1016/J.CNSNS.2012.03.025
review text: The paper deals with the large amplitude limit cycles and their frequency of the planar autonomous systems NEWLINE\[NEWLINE\dot{x}=P(x,y,\lambda),\;\dot{y}=Q(x,y,\lambda),NEWLINE\]NEWLINE where \(P(x,y,\lambda)\) and \(Q(x,y,\lambda)\) are analytic functions of theirs variables, \(x\) and \(y\) are the phase variables and \(\lambda\) is the control parameter. By applying the homotopy analysis method proposed by \textit{S. Liao} [Int. J. Numer. Methods Fluids 14, No. 10, 1173--1191 (1992; Zbl 0754.76065)] the authors deduce analytical approximations of limit cycles and their frequencies in mentioned self-excited systems with strong nonlinearity. As an example, a Rosenzweig-MacArthur predator-prey model is studied in details. The high accuracy of the analytical results are illustrated by comparing with those of numerical integrations.
reviewed by: Alexander Grin
description: scientific article; zbMATH DE number 6081965