Dynamical system of a time-delayed ϕ 6-Van der Pol oscillator: a non-perturbative approach
Abstract A remarkable example of how to quantitatively explain the nonlinear performance of many phenomena in physics and engineering is the Van der Pol oscillator. Therefore, the current paper examines the stability analysis of the dynamics of ϕ 6-Van der Pol oscillator (PHI6) exposed to exterior e...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-07-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-38679-5 |
| _version_ | 1797769491350814720 |
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| author | Galal M. Moatimid T. S. Amer |
| author_facet | Galal M. Moatimid T. S. Amer |
| author_sort | Galal M. Moatimid |
| collection | DOAJ |
| description | Abstract A remarkable example of how to quantitatively explain the nonlinear performance of many phenomena in physics and engineering is the Van der Pol oscillator. Therefore, the current paper examines the stability analysis of the dynamics of ϕ 6-Van der Pol oscillator (PHI6) exposed to exterior excitation in light of its motivated applications in science and engineering. The emphasis in many examinations has shifted to time-delayed technology, yet the topic of this study is still quite significant. A non-perturbative technique is employed to obtain some improvement and preparation for the system under examination. This new methodology yields an equivalent linear differential equation to the exciting nonlinear one. Applying a numerical approach, the analytical solution is validated by this approach. This novel approach seems to be impressive and promising and can be employed in various classes of nonlinear dynamical systems. In various graphs, the time histories of the obtained results, their varied zones of stability, and their polar representations are shown for a range of natural frequencies and other influencing factor values. Concerning the approximate solution, in the case of the presence/absence of time delay, the numerical approach shows excellent accuracy. It is found that as damping and natural frequency parameters increase, the solution approaches stability more quickly. Additionally, the phase plane is more positively impacted by the initial amplitude, external force, damping, and natural frequency characteristics than the other parameters. To demonstrate how the initial amplitude, natural frequency, and cubic nonlinear factors directly affect the periodicity of the resulting solution, many polar forms of the corresponding equation have been displayed. Furthermore, the stable configuration of the analogous equation is shown in the absence of the stimulated force. |
| first_indexed | 2024-03-12T21:09:50Z |
| format | Article |
| id | doaj.art-37be57867d354f0daa6d3e7819c5acdb |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-12T21:09:50Z |
| publishDate | 2023-07-01 |
| publisher | Nature Portfolio |
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| spelling | doaj.art-37be57867d354f0daa6d3e7819c5acdb2023-07-30T11:15:43ZengNature PortfolioScientific Reports2045-23222023-07-0113111410.1038/s41598-023-38679-5Dynamical system of a time-delayed ϕ 6-Van der Pol oscillator: a non-perturbative approachGalal M. Moatimid0T. S. Amer1Department of Mathematics, Faculty of Education, Ain Shams UniversityDepartment of Mathematics, Faculty of Science, Tanta UniversityAbstract A remarkable example of how to quantitatively explain the nonlinear performance of many phenomena in physics and engineering is the Van der Pol oscillator. Therefore, the current paper examines the stability analysis of the dynamics of ϕ 6-Van der Pol oscillator (PHI6) exposed to exterior excitation in light of its motivated applications in science and engineering. The emphasis in many examinations has shifted to time-delayed technology, yet the topic of this study is still quite significant. A non-perturbative technique is employed to obtain some improvement and preparation for the system under examination. This new methodology yields an equivalent linear differential equation to the exciting nonlinear one. Applying a numerical approach, the analytical solution is validated by this approach. This novel approach seems to be impressive and promising and can be employed in various classes of nonlinear dynamical systems. In various graphs, the time histories of the obtained results, their varied zones of stability, and their polar representations are shown for a range of natural frequencies and other influencing factor values. Concerning the approximate solution, in the case of the presence/absence of time delay, the numerical approach shows excellent accuracy. It is found that as damping and natural frequency parameters increase, the solution approaches stability more quickly. Additionally, the phase plane is more positively impacted by the initial amplitude, external force, damping, and natural frequency characteristics than the other parameters. To demonstrate how the initial amplitude, natural frequency, and cubic nonlinear factors directly affect the periodicity of the resulting solution, many polar forms of the corresponding equation have been displayed. Furthermore, the stable configuration of the analogous equation is shown in the absence of the stimulated force.https://doi.org/10.1038/s41598-023-38679-5 |
| spellingShingle | Galal M. Moatimid T. S. Amer Dynamical system of a time-delayed ϕ 6-Van der Pol oscillator: a non-perturbative approach Scientific Reports |
| title | Dynamical system of a time-delayed ϕ 6-Van der Pol oscillator: a non-perturbative approach |
| title_full | Dynamical system of a time-delayed ϕ 6-Van der Pol oscillator: a non-perturbative approach |
| title_fullStr | Dynamical system of a time-delayed ϕ 6-Van der Pol oscillator: a non-perturbative approach |
| title_full_unstemmed | Dynamical system of a time-delayed ϕ 6-Van der Pol oscillator: a non-perturbative approach |
| title_short | Dynamical system of a time-delayed ϕ 6-Van der Pol oscillator: a non-perturbative approach |
| title_sort | dynamical system of a time delayed ϕ 6 van der pol oscillator a non perturbative approach |
| url | https://doi.org/10.1038/s41598-023-38679-5 |
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