Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator
Extreme multistability has frequently been reported in autonomous circuits involving memory-circuit elements, since these circuits possess line/plane equilibrium sets. However, this special phenomenon has rarely been discovered in non-autonomous circuits. Luckily, extreme multistability is found in...
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/5/754 |
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| author | Bei Chen Xinxin Cheng Han Bao Mo Chen Quan Xu |
| author_facet | Bei Chen Xinxin Cheng Han Bao Mo Chen Quan Xu |
| author_sort | Bei Chen |
| collection | DOAJ |
| description | Extreme multistability has frequently been reported in autonomous circuits involving memory-circuit elements, since these circuits possess line/plane equilibrium sets. However, this special phenomenon has rarely been discovered in non-autonomous circuits. Luckily, extreme multistability is found in a simple non-autonomous memcapacitive oscillator in this paper. The oscillator only contains a memcapacitor, a linear resistor, a linear inductor, and a sinusoidal voltage source, which are connected in series. The memcapacitive system model is firstly built for further study. The equilibrium points of the memcapacitive system evolve between a no equilibrium point and a line equilibrium set with the change in time. This gives rise to the emergence of extreme multistability, but the forming mechanism is not clear. Thus, the incremental integral method is employed to reconstruct the memcapacitive system. In the newly reconstructed system, the number and stability of the equilibrium points have complex time-varying characteristics due to the presence of fold bifurcation. Furthermore, the forming mechanism of the extreme multistability is further explained. Note that the initial conditions of the original memcapacitive system are mapped onto the controlling parameters of the newly reconstructed system. This makes it possible to achieve precise control of the extreme multistability. Furthermore, an analog circuit is designed for the reconstructed system, and then PSIM circuit simulations are performed to verify the numerical results. |
| first_indexed | 2024-03-09T20:31:27Z |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T20:31:27Z |
| publishDate | 2022-02-01 |
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| spelling | doaj.art-c7a464e0051f48f29f1001c2136407ca2023-11-23T23:23:08ZengMDPI AGMathematics2227-73902022-02-0110575410.3390/math10050754Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive OscillatorBei Chen0Xinxin Cheng1Han Bao2Mo Chen3Quan Xu4School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, ChinaSchool of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, ChinaSchool of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, ChinaSchool of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, ChinaSchool of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, ChinaExtreme multistability has frequently been reported in autonomous circuits involving memory-circuit elements, since these circuits possess line/plane equilibrium sets. However, this special phenomenon has rarely been discovered in non-autonomous circuits. Luckily, extreme multistability is found in a simple non-autonomous memcapacitive oscillator in this paper. The oscillator only contains a memcapacitor, a linear resistor, a linear inductor, and a sinusoidal voltage source, which are connected in series. The memcapacitive system model is firstly built for further study. The equilibrium points of the memcapacitive system evolve between a no equilibrium point and a line equilibrium set with the change in time. This gives rise to the emergence of extreme multistability, but the forming mechanism is not clear. Thus, the incremental integral method is employed to reconstruct the memcapacitive system. In the newly reconstructed system, the number and stability of the equilibrium points have complex time-varying characteristics due to the presence of fold bifurcation. Furthermore, the forming mechanism of the extreme multistability is further explained. Note that the initial conditions of the original memcapacitive system are mapped onto the controlling parameters of the newly reconstructed system. This makes it possible to achieve precise control of the extreme multistability. Furthermore, an analog circuit is designed for the reconstructed system, and then PSIM circuit simulations are performed to verify the numerical results.https://www.mdpi.com/2227-7390/10/5/754extreme multistabilityinitial conditionmemcapacitive circuitnon-autonomousreconstructed system |
| spellingShingle | Bei Chen Xinxin Cheng Han Bao Mo Chen Quan Xu Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator Mathematics extreme multistability initial condition memcapacitive circuit non-autonomous reconstructed system |
| title | Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator |
| title_full | Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator |
| title_fullStr | Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator |
| title_full_unstemmed | Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator |
| title_short | Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator |
| title_sort | extreme multistability and its incremental integral reconstruction in a non autonomous memcapacitive oscillator |
| topic | extreme multistability initial condition memcapacitive circuit non-autonomous reconstructed system |
| url | https://www.mdpi.com/2227-7390/10/5/754 |
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