Active Control of Chaotic Oscillations in Nonlinear Chemical Dynamics - Journal of Applied Mathematics and Physics

JAMP > Vol.7 No.3, March 2019

Active Control of Chaotic Oscillations in Nonlinear Chemical Dynamics ()

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Download as PDF (Size: 3177KB) PP. 547-558

DOI: 10.4236/jamp.2019.73040 721 Downloads 1,656 Views Citations

Author(s)

Dagbégnon Luc Olabodé^1*, Batablinlè Lamboni², Jean Bio Chabi Orou¹

Affiliation(s)

¹Laboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB); Institut de Mathématiques et de Sciences Physiques (IMSP), Porto-Novo, Bénin.
²Institut de Mathématiques et de Sciences Physiques (IMSP), Porto-Novo, Bénin.

ABSTRACT

Abstract: This work studies the active control of chemical oscillations governed by a forced modified Van der Pol-Duffing oscillator. We considered the dynamics of nonlinear chemical systems subjected to an external sinusoidal excitation. The approximative solution to the first order of the modified Van der Pol-Duffing oscillator is found using the Lindstedt’s perturbation method. The harmonic balance method is used to find the amplitudes of the oscillatory states of the system under control. The effects of the constraint parameter and the control parameter of the model on the amplitude of oscillations are presented. The effects of the active control on the behaviors of the model are analyzed and it appears that with the appropriate selection of the coupling parameter, the chaotic behavior of the model has given way to periodic movements. Numerical simulations are used to validate and complete the analytical results obtained.

KEYWORDS

Forced Modified Van der Pol-Duffing Oscillator, Chemical Dynamics, Active Control and Bifurcations

Share and Cite:

Olabodé, D. , Lamboni, B. and Orou, J. (2019) Active Control of Chaotic Oscillations in Nonlinear Chemical Dynamics. Journal of Applied Mathematics and Physics, 7, 547-558. doi: 10.4236/jamp.2019.73040.

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