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research-article

Analytical solutions of period-1 to period-2 motions in a periodically diffused Brusselator

[+] Author and Article Information
Albert C.J. Luo

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA
aluo@siue.edu

Siyu Guo

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA
sguo@siue.edu

1Corresponding author.

ASME doi:10.1115/1.4038204 History: Received August 03, 2017; Revised October 05, 2017

Abstract

In this paper, the analytical solutions of periodic evolutions of the periodically diffused Brusselator are obtained through the general harmonic balanced method. Stable and unstable solutions of period-1 and period-2 evolutions in the Brusselator are discussed. Stability and bifurcations of the periodic evolution are determined by the eigenvalue analysis, and the corresponding Hopf bifurcations are presented on the analytical bifurcation tree of periodic motion. Numerical simulations of stable period-1 and period-2 motions of Brusselator are completed. The harmonic amplitude spectrums show harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions can be prescribed specifically.

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