Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos
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 the Cardan’s method. Hopf bifurcation has been also...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/8823458 |
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| author | A. V. Monwanou A. A. Koukpémèdji C. Ainamon P. R. Nwagoum Tuwa C. H. Miwadinou J. B. Chabi Orou |
| author_facet | A. V. Monwanou A. A. Koukpémèdji C. Ainamon P. R. Nwagoum Tuwa C. H. Miwadinou J. B. Chabi Orou |
| author_sort | A. V. Monwanou |
| collection | DOAJ |
| description | 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 the Cardan’s method. Hopf bifurcation has been also successfully checked. Routes to chaos have been investigated through bifurcations structures, Lyapunov exponent, phase portraits, and Poincaré section. 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) and g≠0 with Ω=ω and Ω/w≠p/q; p and q are simple positive integers. Vibrational resonance (VR), hysteresis, and coexistence of several attractors have been studied in detail based on the relationship between the frequencies of the AM force. Results of analytical investigations are validated and complemented by numerical simulations. |
| format | Article |
| id | doaj-art-d5c9b4c6d9a1457090c32fdfda7a23f4 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-d5c9b4c6d9a1457090c32fdfda7a23f42025-02-03T06:47:00ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/88234588823458Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and ChaosA. V. Monwanou0A. A. Koukpémèdji1C. Ainamon2P. R. Nwagoum Tuwa3C. H. Miwadinou4J. B. Chabi Orou5Laboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, BeninLaboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, BeninLaboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, BeninLaboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, BeninLaboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, BeninLaboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, BeninThis 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 the Cardan’s method. Hopf bifurcation has been also successfully checked. Routes to chaos have been investigated through bifurcations structures, Lyapunov exponent, phase portraits, and Poincaré section. 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) and g≠0 with Ω=ω and Ω/w≠p/q; p and q are simple positive integers. Vibrational resonance (VR), hysteresis, and coexistence of several attractors have been studied in detail based on the relationship between the frequencies of the AM force. Results of analytical investigations are validated and complemented by numerical simulations.http://dx.doi.org/10.1155/2020/8823458 |
| spellingShingle | A. V. Monwanou A. A. Koukpémèdji C. Ainamon P. R. Nwagoum Tuwa C. H. Miwadinou J. B. Chabi Orou Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos Complexity |
| title | Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos |
| title_full | Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos |
| title_fullStr | Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos |
| title_full_unstemmed | Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos |
| title_short | Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos |
| title_sort | nonlinear dynamics in a chemical reaction under an amplitude modulated excitation hysteresis vibrational resonance multistability and chaos |
| url | http://dx.doi.org/10.1155/2020/8823458 |
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