Symplectic Dynamics and Simultaneous Resonance Analysis of Memristor Circuit Based on Its van der Pol Oscillator
A non-autonomous memristor circuit based on van der Pol oscillator with double periodically forcing term is presented and discussed. Firstly, the differences of the van der Pol oscillation of memristor model between Euler method and symplectic Euler method, four-order Runge–Kutta method (RK4) and fo...
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| Format: | Article |
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MDPI AG
2022-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/6/1251 |
| _version_ | 1797481891393175552 |
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| author | Baonan Yang Zhen Wang Huaigu Tian Jindong Liu |
| author_facet | Baonan Yang Zhen Wang Huaigu Tian Jindong Liu |
| author_sort | Baonan Yang |
| collection | DOAJ |
| description | A non-autonomous memristor circuit based on van der Pol oscillator with double periodically forcing term is presented and discussed. Firstly, the differences of the van der Pol oscillation of memristor model between Euler method and symplectic Euler method, four-order Runge–Kutta method (RK4) and four-order symplectic Runge–Kutta–Nyström method (SRKN4), symplectic Euler method and RK4 method, and symplectic Euler method and SRKN4 method in preserving structure are compared from theoretical and numerical simulations, the symmetry and structure preserving and numerical stability of symplectic scheme are demonstrated. Moreover, the analytic solution of the primary and subharmonic simultaneous resonance of this system is obtained by using the multi-scale method. Finally, based on the resonance relation of the system, the chaotic dynamics behaviors with different parameters are studied. |
| first_indexed | 2024-03-09T22:21:03Z |
| format | Article |
| id | doaj.art-4c5476f049cb44f48f7b8cc1f54e7b93 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:21:03Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4c5476f049cb44f48f7b8cc1f54e7b932023-11-23T19:13:20ZengMDPI AGSymmetry2073-89942022-06-01146125110.3390/sym14061251Symplectic Dynamics and Simultaneous Resonance Analysis of Memristor Circuit Based on Its van der Pol OscillatorBaonan Yang0Zhen Wang1Huaigu Tian2Jindong Liu3Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source, School of Computer Science, Xijing University, Xi’an 710123, ChinaShaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source, School of Computer Science, Xijing University, Xi’an 710123, ChinaShaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source, School of Computer Science, Xijing University, Xi’an 710123, ChinaShaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source, School of Computer Science, Xijing University, Xi’an 710123, ChinaA non-autonomous memristor circuit based on van der Pol oscillator with double periodically forcing term is presented and discussed. Firstly, the differences of the van der Pol oscillation of memristor model between Euler method and symplectic Euler method, four-order Runge–Kutta method (RK4) and four-order symplectic Runge–Kutta–Nyström method (SRKN4), symplectic Euler method and RK4 method, and symplectic Euler method and SRKN4 method in preserving structure are compared from theoretical and numerical simulations, the symmetry and structure preserving and numerical stability of symplectic scheme are demonstrated. Moreover, the analytic solution of the primary and subharmonic simultaneous resonance of this system is obtained by using the multi-scale method. Finally, based on the resonance relation of the system, the chaotic dynamics behaviors with different parameters are studied.https://www.mdpi.com/2073-8994/14/6/1251memristor circuitsymplectic dynamicssimultaneous resonancevan der Pol oscillator |
| spellingShingle | Baonan Yang Zhen Wang Huaigu Tian Jindong Liu Symplectic Dynamics and Simultaneous Resonance Analysis of Memristor Circuit Based on Its van der Pol Oscillator Symmetry memristor circuit symplectic dynamics simultaneous resonance van der Pol oscillator |
| title | Symplectic Dynamics and Simultaneous Resonance Analysis of Memristor Circuit Based on Its van der Pol Oscillator |
| title_full | Symplectic Dynamics and Simultaneous Resonance Analysis of Memristor Circuit Based on Its van der Pol Oscillator |
| title_fullStr | Symplectic Dynamics and Simultaneous Resonance Analysis of Memristor Circuit Based on Its van der Pol Oscillator |
| title_full_unstemmed | Symplectic Dynamics and Simultaneous Resonance Analysis of Memristor Circuit Based on Its van der Pol Oscillator |
| title_short | Symplectic Dynamics and Simultaneous Resonance Analysis of Memristor Circuit Based on Its van der Pol Oscillator |
| title_sort | symplectic dynamics and simultaneous resonance analysis of memristor circuit based on its van der pol oscillator |
| topic | memristor circuit symplectic dynamics simultaneous resonance van der Pol oscillator |
| url | https://www.mdpi.com/2073-8994/14/6/1251 |
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