Multistability and its Annihilation in the Chua’s Oscillator with Piecewise-Linear Nonlinearity
This contribution uncovers numerical evidence of hysteric dynamical behaviors for the same set of the circuit parameters of the Chua’s circuit with traditional piecewise-linear nonlinearity. Stationary points and the symmetry property of the model first forecast the possible evidence of coexisting a...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Akif AKGUL
2020-11-01
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| Series: | Chaos Theory and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/1191711 |
| _version_ | 1797295303654637568 |
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| author | Zeric Njıtacke Théophile Fozin Léandre Kamdjeu Kengne Gervais Leutcho, Jacques Kengne Edwige Mache Kengne |
| author_facet | Zeric Njıtacke Théophile Fozin Léandre Kamdjeu Kengne Gervais Leutcho, Jacques Kengne Edwige Mache Kengne |
| author_sort | Zeric Njıtacke |
| collection | DOAJ |
| description | This contribution uncovers numerical evidence of hysteric dynamical behaviors for the same set of the circuit parameters of the Chua’s circuit with traditional piecewise-linear nonlinearity. Stationary points
and the symmetry property of the model first forecast the possible evidence of coexisting attractors. Then,
well known nonlinear analysis approach based on the bifurcation diagrams, two-parameter diagrams, phase
portraits, two parameter Lyapunov exponent diagrams, graph of maximum Lyapunov exponents, and attraction basins are exploited to characterize the dynamical behavior of the oscillator including coexisting orbits. Finally, the simultaneous existence of both periodic and chaotic orbits highlighted in the Chua’s oscillator is also annihilated based on linear controller. Numerical findings indicate control method ’s efficacy by combining two periodic routes and one chaotic route with another chaotic route. |
| first_indexed | 2024-03-07T21:45:46Z |
| format | Article |
| id | doaj.art-ca857b2301894c6fbffb23c1a00662f8 |
| institution | Directory Open Access Journal |
| issn | 2687-4539 |
| language | English |
| last_indexed | 2024-03-07T21:45:46Z |
| publishDate | 2020-11-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj.art-ca857b2301894c6fbffb23c1a00662f82024-02-25T19:10:01ZengAkif AKGULChaos Theory and Applications2687-45392020-11-012277891971Multistability and its Annihilation in the Chua’s Oscillator with Piecewise-Linear NonlinearityZeric Njıtacke0Théophile Fozin1Léandre Kamdjeu Kengne2Gervais Leutcho,3Jacques Kengne4Edwige Mache Kengne5University of BueaUniversity of BueaUniversity of DschangUniversity of MonsUniversity of DschangUniversity of DschangThis contribution uncovers numerical evidence of hysteric dynamical behaviors for the same set of the circuit parameters of the Chua’s circuit with traditional piecewise-linear nonlinearity. Stationary points and the symmetry property of the model first forecast the possible evidence of coexisting attractors. Then, well known nonlinear analysis approach based on the bifurcation diagrams, two-parameter diagrams, phase portraits, two parameter Lyapunov exponent diagrams, graph of maximum Lyapunov exponents, and attraction basins are exploited to characterize the dynamical behavior of the oscillator including coexisting orbits. Finally, the simultaneous existence of both periodic and chaotic orbits highlighted in the Chua’s oscillator is also annihilated based on linear controller. Numerical findings indicate control method ’s efficacy by combining two periodic routes and one chaotic route with another chaotic route.https://dergipark.org.tr/en/download/article-file/1191711chua’s oscillatorchaotic systemspiecewise-linear nonlinearitymultistability controlmerging crisis |
| spellingShingle | Zeric Njıtacke Théophile Fozin Léandre Kamdjeu Kengne Gervais Leutcho, Jacques Kengne Edwige Mache Kengne Multistability and its Annihilation in the Chua’s Oscillator with Piecewise-Linear Nonlinearity Chaos Theory and Applications chua’s oscillator chaotic systems piecewise-linear nonlinearity multistability control merging crisis |
| title | Multistability and its Annihilation in the Chua’s Oscillator with Piecewise-Linear Nonlinearity |
| title_full | Multistability and its Annihilation in the Chua’s Oscillator with Piecewise-Linear Nonlinearity |
| title_fullStr | Multistability and its Annihilation in the Chua’s Oscillator with Piecewise-Linear Nonlinearity |
| title_full_unstemmed | Multistability and its Annihilation in the Chua’s Oscillator with Piecewise-Linear Nonlinearity |
| title_short | Multistability and its Annihilation in the Chua’s Oscillator with Piecewise-Linear Nonlinearity |
| title_sort | multistability and its annihilation in the chua s oscillator with piecewise linear nonlinearity |
| topic | chua’s oscillator chaotic systems piecewise-linear nonlinearity multistability control merging crisis |
| url | https://dergipark.org.tr/en/download/article-file/1191711 |
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