Dynamics and active control of chemical oscillations modeled as a forced generalized Rayleigh oscillator with asymmetric potential

  • Authors

    • ADECHINAN Adébiyi Joseph Université Nationale des Sciences, Technologie, Ingénierie et Mathématique
    • Kpomahou Y. J. Fernando Université Nationale des Sciences, Technologie, Ingénierie et Mathématique
    • Miwadinou H. Clément Université Nationale des Sciences, Technologie, Ingénierie et Mathématique
    • Hinvi A. laurent Université Nationale des Sciences, Technologie, Ingénierie et Mathématique
  • Chemical oscillations, Generalized Rayleigh oscillator, Melnikov chaos, Coexisting attractors, Active control.
  • This paper focuses on the dynamics and active control of chemical oscillations governed by a forced generalized Rayleigh oscillator. The Melnikov method is used to analytically determine the critical parameters for the onset of chaotic motions. The analytical results are confirmed by numerical simulations. The bifurcation structures obtained show that the model displays a rich variety of dynamical behaviors and remarkable routes to chaos. The effects of the control gain parameters on the behavior of the system are analyzed and the results obtained have shown the control efficiency.

  • References

    1. [1] Epstein IR, Pojman JA (1998) An introduction to nonlinear chemical dynamics, Oxford University Press; 1st edition

      [2] Epstein IR (2003) Nonlinear Chemical Dynamics, Dalton Transactions 34(7) DOI:10.1039/B210932H

      [3] Buchler JR, Einchhorn H (1987) Chaotic Phenomena in Astrophysics, Annals of the New York Academy of Sciences, 497

      [4] Ghosh S, Ray DS (2014) Linenard-type chemical oscillator, The European Physical Journal B, .87(65), 1-7

      [5] Nayfey AH, Mook DT (1995) Nonlinear Oscillations, Nonlinear and Complex Systems, John Wiley and Sons

      [6] Garnett PW (1997) Chaos Theory Tamed, Joseph HENRY Press

      [7] Hayashi C (1964) Nonlinear Oscillations in Physical Systems, Princeton University Press, https://www.jstor.org/stable/j.ctt7zv6k6

      [8] Fröhlich H, Kremer F (1983) Coherent Excitations in Biological Systems, SpringerVerlag

      [9] Nana Nbendjo BR, Yamapi R (2007) Active control of extended Van der Pol equation, Commun, Nonlinear Sci. Numer.Simul, 12; 1550-1559.

      [10] Fathei A, Menzinger M (1997) Stirring effects and phase-dependent inhomogeneity in chemical oscillations: The Belousov–Zhabotinsky reaction in a CSTR, J. Phys. Chem., 101(12), 2304–2309.

      [11] Gruebele M, Wolynes PG (2004) Vibrational energy flow and chemical reactions, Accounts of Chemical Research, 37(4), 261-267.

      [12] Sarkar P, Ray DS (2019) Vibrational antiresonance in nonlinear coupled systems, Physical Review E, Vol. 99, pp.1-7, DOI:https://doi.org/10.1103/PhysRevE.99.052221

      [13] Strogatz SHK (2001) Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Westview Press.

      [14] Landa PS, McClintock PVE (2000), Vibrational resonance, Journal of Physics A: Mathematical General, 33(45), 433-438.

      [15] Soliman MS (1998) Basin boundaries with fractal and smooth accumulation properties in systems with single potential well, Chaos, Solitons & Fractals, 9(6).

      [16] Bao BC, Jiang T, Xu Q, Chen M, Wu HG, Hu YH (2016) Coexisting infinitely many attractors in active band-pass filter-based memristive circuit, Nonlinear Dynamics, 83(3),1711–1723.

      [17] Patidar V, Sharma A, Purohit G (2016) Dynamical behavior of paramerically driven Duffing and externally driven Helmholtz-Duffing oscillators under nonlinear dissipation, Nonlinear Dynamics, 83(3), 75–88.

      [18] Siewe MS, Cao H, Sanjuan MAF (2009) Effect ofnonlinear dissipation on the basin boundaries of a driven two-well Rayleigh-Duffing oscillator, Chaos, Solitons & Fractal, 39(10), 92-99.

      [19] Kaviya B, Suresh R, Chandrasekar VK, Balachandran B (2020) Influence of dissipation on extremeoscillations of a forced anharmonic oscillator, International Journal of Non-Linear Mechanics, pp.1–15.

      [20] Kitio Kwuimy CA, Nataraj C (2011) Melnikov’s criteria, Parametric control of chaos, and stationary chaos occurrence in systems with asymmetric potential subjected to multiscale type excitation, Chaos, .21, 1–12.

      [21] Olabode DL, Miwadinou CH, Monwanou AV, Chabi Orou JB (2018) Horseshoes chaos and its passive control in dissipative nonlinear chemical dynamics, Phys. Scr, 93, 1–12.

      [22] Olabode DL, Miwadinou CH, Monwanou VA, Chabi Orou JB (2019) Effects of passive hydrodynamics force on harmonic and chaotic oscillations in nonlinear chemical dynamics, Physica D., 386, 49-59.

      [23] Olabode DL, Lamboni B, Chabi Orou JB (2019) Active control of chaotic oscillations in nonlinear chemical dynamics, Journal of Applied Mathematics and Physics, 7, 547-558.

      [24] EnjieuKadji H G, Nana Nbendjo BR (2012) Melnikov’s criteria, Passive aerodynamics control of plasma instabilities, Commun Nonlinear Sci Numer Simulat, 17, 1779-1794.

      [25] Sambas A, Vaidyanathan S, Diandra CF, Mohamed MA, Trisnawan, Purwandari D (2018) A New Two-Wing Chaotic System with Line Equilibrium,its Analysis, Adaptive Synchronization and Circuit Simulation International Journal of Engineering & Technology, 7(4), 3739-3746.

      [26] Monwanou AV, Koukpemédji AA, Ainamon C, Nwagoum Tuwa PR, Miwadinou CH, Chabi Orou JB (2020) Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos Complexity, Article ID, 1-16.

      [27] Fangnon R, Ainamon C, Monwanou AV, Miwadinou CH, Chabi Orou JB (2020) Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator Complexity, Article ID, 1-17.

      [28] Boissonade J, De Keppe P (1980) Transitions from Bistability to Limit Cycle Oscillations Theoretical Analysis and Experimental Evidence in an Open Chemical System Phys. Chem, 84, 501-506.

      [29] Epstein IR, Showalter K (1996) Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos, J. Phys. Chem., 100(13), 132-13147.

      [30] Belousov BP (1985) In Oscillations and Travelling Waves in Chemical Systems, Wiley.

      [31] Miwadinou CH, Monwanou AV, Yovogan J, Hinvi L.A, Nwagoum Tuwa PR, Chabi Orou JB (2018) Modeling nonlinear dissipative chemical dynamics by a forced modified Van der Pol-Duffing oscillator with asymmetric potential: chaotic behaviors predictions, Chinese Journal of Physics, 56(3), 1089-1104.

      [32] Kpomahou YJF, Hinvi LA, Adéchinan JA, Miwadinou CH (2021) Chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations, Complexity, Article ID, 1-18.

      [33] Kpomahou YJF, Adéchinan AJ (2021) Nonlinear dynamics and active control in a Liénard-type oscillator under parametric and external periodic excitations, ´ American Journal of Computational and Applied Mathematics, 10(2), 48-61.

      [34] Melnikov VK (1963) On the stability of the center for time periodic perturbations, Transactions of the Moscow Mathematical Society, 12(1), 1-57.

      [35] Cicogna G, Papoff F (1987) Asymmetric doffing equation and the appearance of chaos, Euro phys. Let, 3(9), 963-967.

      [36] Gradshteyn IS, Ryzhik IM (2007) Table of Integrals, Series, and Products, Academic Press.

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  • How to Cite

    Adébiyi Joseph, A., Y. J. Fernando, K., H. Clément, M., & A. laurent, H. (2021). Dynamics and active control of chemical oscillations modeled as a forced generalized Rayleigh oscillator with asymmetric potential. International Journal of Basic and Applied Sciences, 10(2), 20-31. https://doi.org/10.14419/ijbas.v10i2.31631