Chaotic Dynamics of a Mixed Rayleigh–Liénard Oscillator Driven by Parametric Periodic Damping and External Excitations
In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically. The equilibrium points and their stability evolutions are analytically analyzed, and the transitions of dynamical behavi...
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| Published in | Complexity (New York, N.Y.) Vol. 2021; no. 1 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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2021
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| Abstract | In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically. The equilibrium points and their stability evolutions are analytically analyzed, and the transitions of dynamical behaviors are explored in detail. Furthermore, from the Melnikov method, the analytical criterion for the appearance of the homoclinic chaos is derived. Analytical prediction is tested against numerical simulations based on the basin of attraction of initial conditions. As a result, it is found that for ω=ν, the chaotic region decreases and disappears when the amplitude of the parametric periodic damping excitation increases. Moreover, increasing of F1 and F0 provokes an erosion of the basin of attraction and a modification of the geometrical shape of the chaotic attractors. For ω≠ν and η=0.8, the fractality of the basin of attraction increases as the amplitude of the external periodic excitation and constant term increase. Bifurcation structures of our system are performed through the fourth-order Runge–Kutta ode 45 algorithm. It is found that the system displays a remarkable route to chaos. It is also found that the system exhibits monostable and bistable oscillations as well as the phenomenon of coexistence of attractors. |
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| AbstractList | In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically. The equilibrium points and their stability evolutions are analytically analyzed, and the transitions of dynamical behaviors are explored in detail. Furthermore, from the Melnikov method, the analytical criterion for the appearance of the homoclinic chaos is derived. Analytical prediction is tested against numerical simulations based on the basin of attraction of initial conditions. As a result, it is found that for ω=ν, the chaotic region decreases and disappears when the amplitude of the parametric periodic damping excitation increases. Moreover, increasing of F1 and F0 provokes an erosion of the basin of attraction and a modification of the geometrical shape of the chaotic attractors. For ω≠ν and η=0.8, the fractality of the basin of attraction increases as the amplitude of the external periodic excitation and constant term increase. Bifurcation structures of our system are performed through the fourth-order Runge–Kutta ode 45 algorithm. It is found that the system displays a remarkable route to chaos. It is also found that the system exhibits monostable and bistable oscillations as well as the phenomenon of coexistence of attractors. In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically. The equilibrium points and their stability evolutions are analytically analyzed, and the transitions of dynamical behaviors are explored in detail. Furthermore, from the Melnikov method, the analytical criterion for the appearance of the homoclinic chaos is derived. Analytical prediction is tested against numerical simulations based on the basin of attraction of initial conditions. As a result, it is found that for ω = ν , the chaotic region decreases and disappears when the amplitude of the parametric periodic damping excitation increases. Moreover, increasing of F 1 and F 0 provokes an erosion of the basin of attraction and a modification of the geometrical shape of the chaotic attractors. For ω ≠ ν and η = 0.8, the fractality of the basin of attraction increases as the amplitude of the external periodic excitation and constant term increase. Bifurcation structures of our system are performed through the fourth‐order Runge–Kutta ode 45 algorithm. It is found that the system displays a remarkable route to chaos. It is also found that the system exhibits monostable and bistable oscillations as well as the phenomenon of coexistence of attractors. |
| Author | Hinvi, Laurent Amoussou Adéchinan, Joseph Adébiyi Miwadinou, Clément Hodévèwan Kpomahou, Yélomè Judicaël Fernando |
| Author_xml | – sequence: 1 givenname: Yélomè Judicaël Fernando orcidid: 0000-0003-4496-818X surname: Kpomahou fullname: Kpomahou, Yélomè Judicaël Fernando organization: Department of Industrial and Technical SciencesLARPETENSET-LokossaUniversité Nationale des Sciences, TechnologiesIngénierie et Mathématiques-AbomeyAbomeyBenin – sequence: 2 givenname: Laurent Amoussou surname: Hinvi fullname: Hinvi, Laurent Amoussou organization: Département de Génie Mécanique et Productique (GMP)Institut National Supérieur de Technologie Industrielle (INSTI) Lokossa/UNSTIM-AbomeyAbomeyBenin – sequence: 3 givenname: Joseph Adébiyi surname: Adéchinan fullname: Adéchinan, Joseph Adébiyi organization: Department of PhysicsFAST-NatitingouUniversité Nationale des Sciences, TechnologiesIngénierie et Mathématiques-AbomeyAbomeyBenin – sequence: 4 givenname: Clément Hodévèwan orcidid: 0000-0001-9369-9583 surname: Miwadinou fullname: Miwadinou, Clément Hodévèwan organization: Department of PhysicsENS-NatitingouUniversité Nationale des Sciences, TechnologiesIngénierie et Mathématiques-AbomeyAbomeyBenin |
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| Copyright | Copyright © 2021 Yélomè Judicaël Fernando Kpomahou et al. Copyright © 2021 Yélomè Judicaël Fernando Kpomahou et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Accuracy Algorithms Amplitudes Attraction Behavior Chaos theory Circuits Damping Dynamic stability Dynamical systems Eigenvalues Equilibrium Excitation Initial conditions Mathematical analysis Ordinary differential equations Oscillators Runge-Kutta method Stability analysis Vibration |
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| Title | Chaotic Dynamics of a Mixed Rayleigh–Liénard Oscillator Driven by Parametric Periodic Damping and External Excitations |
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