In this paper, the analytical solutions of periodic evolutions of the periodically diffused Brusselator are obtained through the generalized harmonic balanced method. Stable and unstable solutions of period-1 and period-2 evolutions in the Brusselator are presented. 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 the periodic motions. Numerical simulations of stable period-1 and period-2 motions of Brusselator are completed. The harmonic amplitude spectra show harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions can be prescribed specifically.
Analytical Solutions of Period-1 to Period-2 Motions in a Periodically Diffused Brusselator
Southern Illinois University Edwardsville,
Edwardsville, IL 62026-1805
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 3, 2017; final manuscript received October 5, 2017; published online July 26, 2018. Assoc. Editor: Hiroshi Yabuno.
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Luo, A. C. J., and Guo, S. (July 26, 2018). "Analytical Solutions of Period-1 to Period-2 Motions in a Periodically Diffused Brusselator." ASME. J. Comput. Nonlinear Dynam. September 2018; 13(9): 090912. https://doi.org/10.1115/1.4038204
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