Geodesic
Effect of an amplitude modulated force on vibrational resonance, chaos, and multistability in a modified Van der Pol-Duffing oscillator
Miwadinou, C. H. 1 ; Hinvi, L. A. 2 ; Ainamon, C. 3 ; Monwanou, A. V. 3
1 Laboratoire de Mecanique des Fluides, de la Dynamique Nonlineaire et de la Modelisation des Systemes Biologiques (LMFDNMSB), Institut de Mathematiques et de Sciences Physiques, Porto-Novo, Benin;Departement de Physique, ENS-Natitingou, Universite Nationale des Sciences, Technologies, Ingenierie et Mathematiques (UNSTIM), Abomey, Benin
2 Laboratoire de Mecanique des Fluides, de la Dynamique Nonlineaire et de la Modelisation des Systemes Biologiques (LMFDNMSB), Institut de Mathematiques et de Sciences Physiques, Porto-Novo, Benin;Departement de Genie Mecanique et Productique GMP, INSTI-Lokossa, Universite Nationale des Sciences, Technologies, Ingenierie et Mathematiques (UNSTIM), Abomey, Benin
3 Laboratoire de Mecanique des Fluides, de la Dynamique Nonlineaire et de la Modelisation des Systemes Biologiques (LMFDNMSB), Institut de Mathematiques et de Sciences Physiques, Porto-Novo, Benin
Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 2, p. 111-122.

Voir la notice de l'article provenant de la source International Scientific Research Publications

This paper deals with the effects of an amplitude modulated (AM) excitation on the nonlinear dynamics of reactions between four molecules. The computation of the fixed points of the autonomous nonlinear chemical system has been made in detail using Cardan's method. Routes to chaos have been investigated through bifurcations structures, Lyapunov exponent and phase portraits. The effects of the control force on chaotic motions have been strongly analyzed and the control efficiency is found in the cases $g=0$ (unmodulated case), $g\neq 0$ with $\Omega=n\omega$; $n$ a natural number and $\frac{\Omega}{\omega}\neq\frac{p}{q}$; $p$ and $q$ are simple positive integers. Vibrational Resonance (VR), hysteresis and coexistence of several attractors have been studied in details based on the relationship between the frequencies of the AM force. Results of analytical investigations are validated and complemented by numerical simulations.
DOI : 10.22436/jnsa.016.02.04
Classification : 34H10, 92E20, 37N99, 34C28
Keywords: Modified Van der Pol oscillator, Cardan's method, chaos, coexisting attractors, vibrational resonance

Miwadinou, C. H.  1 ; Hinvi, L. A.  2 ; Ainamon, C.  3 ; Monwanou, A. V.  3

1 Laboratoire de Mecanique des Fluides, de la Dynamique Nonlineaire et de la Modelisation des Systemes Biologiques (LMFDNMSB), Institut de Mathematiques et de Sciences Physiques, Porto-Novo, Benin;Departement de Physique, ENS-Natitingou, Universite Nationale des Sciences, Technologies, Ingenierie et Mathematiques (UNSTIM), Abomey, Benin
2 Laboratoire de Mecanique des Fluides, de la Dynamique Nonlineaire et de la Modelisation des Systemes Biologiques (LMFDNMSB), Institut de Mathematiques et de Sciences Physiques, Porto-Novo, Benin;Departement de Genie Mecanique et Productique GMP, INSTI-Lokossa, Universite Nationale des Sciences, Technologies, Ingenierie et Mathematiques (UNSTIM), Abomey, Benin
3 Laboratoire de Mecanique des Fluides, de la Dynamique Nonlineaire et de la Modelisation des Systemes Biologiques (LMFDNMSB), Institut de Mathematiques et de Sciences Physiques, Porto-Novo, Benin 
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     title = {Effect of an amplitude modulated force on vibrational resonance, chaos, and multistability in a modified {Van} der {Pol-Duffing} oscillator},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {111-122},
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Miwadinou, C. H. ; Hinvi, L. A. ; Ainamon, C. ; Monwanou, A. V. . Effect of an amplitude modulated force on vibrational resonance, chaos, and multistability in a modified Van der Pol-Duffing oscillator. Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 2, p. 111-122. doi : 10.22436/jnsa.016.02.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.02.04/

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