Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator

Bei CHEN; Quan XU; Mo CHEN; Huagan WU; Bocheng BAO

doi:10.1631/FITEE.2000622

Your Location：

Home >

Browse articles >

Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator

Regular Papers | Updated：2022-06-06

- Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator
- 忆容振荡器初值切换调控的超级多稳定性及其机理分析
- Frontiers of Information Technology & Electronic Engineering Vol. 22, Issue 11, Pages: 1517-1531(2021)
- Affiliations：
  
  School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China
- Author bio：
  
  Bocheng BAO, E-mail: mervinbao@126.com
- Funds：
- DOI：10.1631/FITEE.2000622
  CLC： O415
- Received：09 September 2020，
  
  Revised：2021-;9-30，
  
  Published：2021-11
- Accepted：
Scan QR Code
Bei CHEN, Quan XU, Mo CHEN, et al. Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(11): 1517-1531.
DOI：

Bei CHEN, Quan XU, Mo CHEN, et al. Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(11): 1517-1531. DOI： 10.1631/FITEE.2000622.

摘要

超级多稳定性以其丰富多样的动力学状态和工程应用中的极大灵活性受到科学家们关注。利用4个线性电路元件和一个具有余弦逆忆容值的非线性荷控型忆容元件，构造了一个四维忆容振荡器。四维忆容振荡器具有一个线平衡集，其稳定性随忆容的初始条件周期性演化。由于周期性演化的稳定性，四维忆容振荡器展现了初值切换调控的超级多稳定性。通过分岔图、李雅普诺夫指数和相轨图，揭示了周期倍增/减半分岔、混沌危机和初值切换共存吸引子的复杂动力学行为。在此基础上，通过积分变换得到一个重构系统，揭示了忆容振荡器中初值切换调控超级多稳定性的形成机理。最后设计了重构系统的实现电路，并进行了PSIM电路仿真，验证了数值分析的有效性。

Abstract

Extreme multistability has seized scientists' attention due to its rich diversity of dynamical behaviors and great flexibility in engineering applications. In this paper

a four-dimensional (4D) memcapacitive oscillator is built using four linear circuit elements and one nonlinear charge-controlled memcapacitor with a cosine inverse memcapacitance. The 4D memcapacitive oscillator possesses a line equilibrium set

and its stability periodically evolves with the initial condition of the memcapacitor. The 4D memcapacitive oscillator exhibits initial-condition-switched boosting extreme multistability due to the periodically evolving stability. Complex dynamical behaviors of period doubling/halving bifurcations

chaos crisis

and initial-condition-switched coexisting attractors are revealed by bifurcation diagrams

Lyapunov exponents

and phase portraits. Thereafter

a reconstructed system is derived via integral transformation to reveal the forming mechanism of the initial-condition-switched boosting extreme multistability in the memcapacitive oscillator. Finally

an implementation circuit is designed for the reconstructed system

and Power SIMulation (PSIM) simulations are executed to confirm the validity of the numerical analysis.

关键词

Keywords

references

A Akgul . . Chaotic oscillator based on fractional order memcapacitor . . J Circ Syst Comput , , 2019 . . 28 ( ( 14 ): ): 1950239 DOI: 10.1142/S0218126619502396 http://doi.org/10.1142/S0218126619502396 . .

BC Bao , , , Q Xu , , , H Bao , , , 等 . . Extreme multistability in a memristive circuit . . Electron Lett , , 2016 . . 52 ( ( 12 ): ): 1008 - - 1010 . . DOI: 10.1049/el.2016.0563 http://doi.org/10.1049/el.2016.0563 . .

BC Bao , , , T Jiang , , , GY Wang , , , 等 . . Two-memristor-based Chua's hyperchaotic circuit with plane equilibrium and its extreme multistability . . Nonl Dynam , , 2017 . . 89 ( ( 2 ): ): 1157 - - 1171 . . DOI: 10.1007/s11071-017-3507-0 http://doi.org/10.1007/s11071-017-3507-0 . .

H Bao , , , N Wang , , , BC Bao , , , 等 . . Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jeck system with four line equilibria . . Commun Nonl Sci Nemer Simul , , 2018 . . 57 264 - - 275 . . DOI: 10.1016/j.cnsns.2017.10.001 http://doi.org/10.1016/j.cnsns.2017.10.001 . .

H Bao , , , M Chen , , , HG Wu , , , 等 . . Memristor initial-boosted coexisting plane bifurcations and its extreme multi-stability reconstitution in two-memristor-based dynamical system . . Sci China Technol Sci , , 2020a . . 63 ( ( 4 ): ): 603 - - 613 . . DOI: 10.1007/s11431-019-1450-6 http://doi.org/10.1007/s11431-019-1450-6 . .

H Bao , , , WB Liu , , , J Ma , , , 等 . . Memristor initial-offset boosting in memristive HR neuron model with hidden firing patterns . . Int J Bifurc Chaos , , 2020b . . 30 ( ( 10 ): ): 2030029 DOI: 10.1142/S0218127420300293 http://doi.org/10.1142/S0218127420300293 . .

E Cagin , , , DY Chen , , , JJ Siddiqui , , , 等 . . Hysteretic metal-ferroelectric-semiconductor capacitors based on PZT/ZnO heterostructures . . J Phys D Appl Phys , , 2007 . . 40 ( ( 8 ): ): 2430 - - 2434 . . DOI: 10.1088/0022-3727/40/8/003 http://doi.org/10.1088/0022-3727/40/8/003 . .

H Chang , , , YX Li , , , GR Chen , , , 等 . . Extreme multistability and complex dynamics of a memristor-based chaotic system . . Int J Bifurc Chaos , , 2020 . . 30 ( ( 8 ): ): 2030019 DOI: 10.1142/S0218127420300190 http://doi.org/10.1142/S0218127420300190 . .

M Chen , , , Y Feng , , , H Bao , , , 等 . . State variable mapping method for studying initial-dependent dynamics in memristive hyper-jerk system with line equilibrium . . Chaos Sol Fract , , 2018 . . 115 313 - - 324 . . DOI: 10.1016/j.chaos.2018.07.025 http://doi.org/10.1016/j.chaos.2018.07.025 . .

M Chen , , , Y Feng , , , H Bao , , , 等 . . Hybrid state variable incremental integral for reconstructing extreme multistability in memristive jerk system with cubic nonlinearity . . Complexity , , 2019a . . 2019 8549472 DOI: 10.1155/2019/8549472 http://doi.org/10.1155/2019/8549472 . .

M Chen , , , X Ren , , , HG Wu , , , 等 . . Periodically varied initial offset boosting behaviors in a memristive system with cosine memductance . . Front Inform Technol Electron Eng , , 2019b . . 20 ( ( 12 ): ): 1706 - - 1716 . . DOI: 10.1631/FITEE.1900360 http://doi.org/10.1631/FITEE.1900360 . .

M Chen , , , X Ren , , , HG Wu , , , 等 . . Interpreting initial offset boosting via reconstitution in integral domain . . Chaos Sol Fract , , 2020 . . 131 109544 DOI: 10.1016/j.chaos.2019.109544 http://doi.org/10.1016/j.chaos.2019.109544 . .

T Driscoll , , , HT Kim , , , BG Chae , , , 等 . . Memory metamaterials . . Science , , 2009 . . 325 ( ( 5947 ): ): 1518 - - 1521 . . DOI: 10.1126/science.1176580 http://doi.org/10.1126/science.1176580 . .

S Khorashadizadeh , , , MH Majidi . . Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications . . Front Inform Technol Electron Eng , , 2018 . . 19 ( ( 9 ): ): 1180 - - 1190 . . DOI: 10.1631/FITEE.1601814 http://doi.org/10.1631/FITEE.1601814 . .

ST Kingni , , , K Rajagopal , , , S Çiçek , , , 等 . . Dynamic analysis, FPGA implementation, and cryptographic application of an autonomous 5D chaotic system with offset boosting . . Front Inform Technol Electron Eng , , 2020 . . 21 ( ( 6 ): ): 950 - - 961 . . DOI: 10.1631/FITEE.1900167 http://doi.org/10.1631/FITEE.1900167 . .

QX Lai , , , L Zhang , , , ZY Li , , , 等 . . Analog memory capacitor based on field-configurable ion-doped polymers . . Appl Phys Lett , , 2009 . . 95 ( ( 21 ): ): 213503 DOI: 10.1063/1.3268433 http://doi.org/10.1063/1.3268433 . .

CB Li , , , JC Sprott . . Variable-boostable chaotic flows . . Optik , , 2016 . . 127 ( ( 22 ): ): 10389 - - 10398 . . DOI: 10.1016/j.ijleo.2016.08.046 http://doi.org/10.1016/j.ijleo.2016.08.046 . .

CB Li , , , WJC Thio , , , HHC Iu , , , 等 . . A memristive chaotic oscillator with increasing amplitude and frequency . . IEEE Access , , 2018 . . 6 12945 - - 12950 . . DOI: 10.1109/ACCESS.2017.2788408 http://doi.org/10.1109/ACCESS.2017.2788408 . .

RX Liu , , , RX Dong , , , SC Qin , , , 等 . . A new type artificial synapse based on the organic copolymer memcapacitor . . Org Electron , , 2020 . . 81 105680 DOI: 10.1016/j.orgel.2020.105680 http://doi.org/10.1016/j.orgel.2020.105680 . .

XJ Ma , , , J Mou , , , J Liu , , , 等 . . A novel simple chaotic circuit based on memristor-memcapacitor . . Nonl Dynam , , 2020 . . 100 ( ( 3 ): ): 2859 - - 2876 . . DOI: 10.1007/s11071-020-05601-x http://doi.org/10.1007/s11071-020-05601-x . .

J Martinez-Rincon , , , YV Pershin . . Bistable nonvolatile elastic-membrane memcapacitor exhibiting a chaotic behavior . . IEEE Trans Electron Dev , , 2011 . . 58 ( ( 6 ): ): 1809 - - 1812 . . DOI: 10.1109/TED.2011.2126022 http://doi.org/10.1109/TED.2011.2126022 . .

J Martinez-Rincon , , , M di Ventra , , , YV Pershin . . Solid-state memcapacitive system with negative and diverging capacitance . . Phys Rev B , , 2010 . . 81 ( ( 19 ): ): 195430 DOI: 10.1103/PhysRevB.81.195430 http://doi.org/10.1103/PhysRevB.81.195430 . .

JS Najem , , , MS Hasan , , , RS Williams , , , 等 . . Dynamical nonlinear memory capacitance in biomimetic membranes . . Nat Commun , , 2019 . . 10 3239 DOI: 10.1038/s41467-019-11223-8 http://doi.org/10.1038/s41467-019-11223-8 . .

YV Pershin , , , MD Ventra . . Memory effects in complex materials and nanoscale systems . . Adv Phys , , 2011 . . 60 ( ( 2 ): ): 145 - - 227 . . DOI: 10.1080/00018732.2010.544961 http://doi.org/10.1080/00018732.2010.544961 . .

YV Pershin , , , FL Traversa , , , M di Ventra . . Memcomputing with membrane memcapacitive systems . . Nanotechnology , , 2015 . . 26 ( ( 22 ): ): 225201 DOI: 10.1088/0957-4484/26/22/225201 http://doi.org/10.1088/0957-4484/26/22/225201 . .

VT Pham , , , A Akgul , , , C Volos , , , 等 . . Dynamics and circuit realization of a no-equilibrium chaotic system with a boostable variable . . AEU-Int J Electron Commun , , 2017 . . 78 134 - - 140 . . DOI: 10.1016/j.aeue.2017.05.034 http://doi.org/10.1016/j.aeue.2017.05.034 . .

AN Pisarchik , , , U Feudel . . Control of multistability . . Phys Rep , , 2014 . . 540 ( ( 4 ): ): 167 - - 218 . . DOI: 10.1016/j.physRep2014.02.007 http://doi.org/10.1016/j.physRep2014.02.007 . .

K Rajagopal , , , A Akgul , , , S Jafari , , , 等 . . A chaotic memcapacitor oscillator with two unstable equilibriums and its fractional form with engineering applications . . Nonl Dynam , , 2018a . . 91 ( ( 2 ): ): 957 - - 974 . . DOI: 10.1007/s11071-017-3921-3 http://doi.org/10.1007/s11071-017-3921-3 . .

K Rajagopal , , , S Jafari , , , A Karthikeyan , , , 等 . . Hyperchaotic memcapacitor oscillator with infinite equilibria and coexisting attractors . . Circ Syst Signal Process , , 2018b . . 37 ( ( 9 ): ): 3702 - - 3724 . . DOI: 10.1007/s00034-018-0750-7 http://doi.org/10.1007/s00034-018-0750-7 . .

JW Sun , , , GY Han , , , YF Wang . . Dynamical analysis of memcapacitor chaotic system and its image encryption application . . Int J Contr Autom Syst , , 2020 . . 18 ( ( 5 ): ): 1242 - - 1249 . . DOI: 10.1007/s12555-019-0015-7 http://doi.org/10.1007/s12555-019-0015-7 . .

GY Wang , , , BZ Cai , , , PP Jin , , , 等 . . Memcapacitor model and its application in a chaotic oscillator . . Chin Phys B , , 2016 . . 25 ( ( 1 ): ): 010503 DOI: 10.1088/1674-1056/25/1/010503 http://doi.org/10.1088/1674-1056/25/1/010503 . .

GY Wang , , , CB Shi , , , XW Wang , , , 等 . . Coexisting oscillation and extreme multistability for a memcapacitor-based circuit . . Math Probl Eng , , 2017a . . 2017 6504969 DOI: 10.1155/2017/6504969 http://doi.org/10.1155/2017/6504969 . .

GY Wang , , , SC Zang , , , XY Wang , , , 等 . . Memcapacitor model and its application in chaotic oscillator with memristor . . Chaos , , 2017b . . 27 ( ( 1 ): ): 013110 DOI: 10.1063/1.4973238 http://doi.org/10.1063/1.4973238 . .

XY Wang , , , J Yu , , , CX Jin , , , 等 . . Chaotic oscillator based on memcapacitor and meminductor . . Nonl Dynam , , 2019 . . 96 ( ( 1 ): ): 161 - - 173 . . DOI: 10.1007/s11071-019-04781-5 http://doi.org/10.1007/s11071-019-04781-5 . .

Z Wang , , , A Akgul , , , VT Pham , , , 等 . . Chaos-based application of a novel no-equilibrium chaotic system with coexisting attractors . . Nonl Dynam , , 2017 . . 89 ( ( 3 ): ): 1877 - - 1887 . . DOI: 10.1007/s11071-017-3558-2 http://doi.org/10.1007/s11071-017-3558-2 . .

HG Wu , , , Y Ye , , , BC Bao , , , 等 . . Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system . . Chaos Sol Fract , , 2019a . . 121 178 - - 185 . . DOI: 10.1016/j.chaos.2019.03.005 http://doi.org/10.1016/j.chaos.2019.03.005 . .

HG Wu , , , Y Ye , , , M Chen , , , 等 . . Periodically switched memristor initial boosting behaviors in memristive hypogenetic jerk system . . IEEE Access , , 2019b . . 7 145022 - - 145029 . . DOI: 10.1109/ACCESS.2019.2945754 http://doi.org/10.1109/ACCESS.2019.2945754 . .

Q Xu , , , Y Lin , , , BC Bao , , , 等 . . Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit . . Chaos Sol Fract , , 2016 . . 83 186 - - 200 . . DOI: 10.1016/j.chaos.2015.12.007 http://doi.org/10.1016/j.chaos.2015.12.007 . .

Q Xu , , , X Tan , , , YZ Zhang , , , 等 . . Riddled attraction basin and multistability in three-element-based memristive circuit . . Complexity , , 2020 . . 2020 4624792 DOI: 10.1155/2020/4624792 http://doi.org/10.1155/2020/4624792 . .

LB Yang , , , QG Yang , , , GR Chen . . Hidden attractors, singularly degenerate heteroclinic orbits, multistability and physical realization of a new 6D hyperchaotic system . . Commun Nonl Sci Numer Simul , , 2020 . . 90 105362 DOI: 10.1016/j.cnsns.2020.105362 http://doi.org/10.1016/j.cnsns.2020.105362 . .

F Yuan , , , YX Li . . A chaotic circuit constructed by a memristor, a memcapacitor and a meminductor . . Chaos , , 2019 . . 29 ( ( 10 ): ): 101101 DOI: 10.1063/1.5125673 http://doi.org/10.1063/1.5125673 . .

F Yuan , , , GY Wang , , , YR Shen , , , 等 . . Coexisting attractors in a memcapacitor-based chaotic oscillator . . Nonl Dynam , , 2016 . . 86 ( ( 1 ): ): 37 - - 50 . . DOI: 10.1007/s11071-016-2870-6 http://doi.org/10.1007/s11071-016-2870-6 . .

F Yuan , , , Y Deng , , , YX Li , , , 等 . . The amplitude, frequency and parameter space boosting in a memristor–meminductor-based circuit . . Nonl Dynam , , 2019a . . 96 ( ( 1 ): ): 389 - - 405 . . DOI: 10.1007/s11071-019-04795-z http://doi.org/10.1007/s11071-019-04795-z . .

F Yuan , , , YX Li , , , GY Wang , , , 等 . . Complex dynamics in a memcapacitor-based circuit . . Entropy , , 2019b . . 21 ( ( 2 ): ): 188 DOI: 10.3390/e21020188 http://doi.org/10.3390/e21020188 . .

S Zhang , , , YC Zeng , , , ZJ Li , , , 等 . . Hidden extreme multistability, antimonotonicity and offset boosting control in a novel fractional-order hyperchaotic system without equilibrium . . Int J Bifurc Chaos , , 2018 . . 28 ( ( 13 ): ): 1850167 DOI: 10.1142/S0218127418501675 http://doi.org/10.1142/S0218127418501675 . .

YZ Zhang , , , Z Liu , , , HG Wu , , , 等 . . Extreme multistability in memristive hyper-jerk system and stability mechanism analysis using dimensionality reduction model . . Eur Phys J Spec Top , , 2019 . . 228 ( ( 10 ): ): 1995 - - 2009 . . DOI: 10.1140/epjst/e2019-800238-0 http://doi.org/10.1140/epjst/e2019-800238-0 . .

L Zhao , , , Z Fan , , , SL Cheng , , , 等 . . An artificial optoelectronic synapse based on a photoelectric memcapacitor . . Adv Electron Mater , , 2020 . . 6 ( ( 2 ): ): 1900858 DOI: 10.1002/aelm.201900858 http://doi.org/10.1002/aelm.201900858 . .

W Zhou , , , GY Wang , , , HHC Iu , , , 等 . . Complex dynamics of a non-volatile memcapacitor-aided hyperchaotic oscillator . . Nonl Dynam , , 2020 . . 100 ( ( 4 ): ): 3937 - - 3957 . . DOI: 10.1007/s11071-020-05722-3 http://doi.org/10.1007/s11071-020-05722-3 . .

Z Zhou , , , DS Yu , , , XY Wang . . Investigation on the dynamic behaviors of the coupled memcapacitor-based circuits . . Chin Phys B , , 2017 . . 26 ( ( 12 ): ): 120701 DOI: 10.1088/1674-1056/26/12/120701 http://doi.org/10.1088/1674-1056/26/12/120701 . .

Views

116

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

Chat

Address：Zhejiang University Press, 148 Tianmushan Road, Hangzhou, China Postal code：310028
Tel：+86-571-88273162 Email：fitee@zju.edu.cn
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰