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ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

On Independent Period-m Evolutions in a Periodically Forced Brusselator

Journal of Vcibration Testing and System Dynamics 2(4) (2018) 375--402 | DOI:10.5890/JVTSD.2018.12.004

Albert C.J. Luo, Siyu Guo

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, IL 62026-1805, USA

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Abstract

In this paper, the analytical solutions of independent period-m evolutions (m=3;5;7;9) of chemical concentrations in a periodically forced Brusselator are obtained through the generalized harmonic balance method. Stability and bifurcation of independent periodic evolutions are determined through eigenvalue analysis. The nonlinear frequency-amplitude characteristics of independent periodic evolutions are discussed. To illustrate the analytical solutions, numerical simulations of stable and unstable period-m evolutions (m = 3;5;7;9) are presented herein. The harmonic amplitude spectrums give an approximate estimation of harmonic effects on analytical solutions of periodic motions.

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