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.
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akgul A, 2019. Chaotic oscillator based on fractional order memcapacitor. J Circ Syst Comput, 28(14):1950239. https://doi.org/10.1142/S0218126619502396
Bao BC, Xu Q, Bao H, et al., 2016. Extreme multistability in a memristive circuit. Electron Lett, 52(12):1008–1010. https://doi.org/10.1049/el.2016.0563
Bao BC, Jiang T, Wang GY, et al., 2017. Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability. Nonl Dynam, 89(2):1157–1171. https://doi.org/10.1007/s11071-017-3507-0
Bao H, Wang N, Bao BC, et al., 2018. Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jeck system with four line equilibria. Commun Nonl Sci Nemer Simul, 57:264–275. https://doi.org/10.1016/j.cnsns.2017.10.001
Bao H, Chen M, Wu HG, et al., 2020a. Memristor initialboosted coexisting plane bifurcations and its extreme multi-stability reconstitution in two-memristor-based dynamical system. Sci China Technol Sci, 63(4):603–613. https://doi.org/10.1007/s11431-019-1450-6
Bao H, Liu WB, Ma J, et al., 2020b. Memristor initial-offset boosting in memristive HR neuron model with hidden firing patterns. Int J Bifurc Chaos, 30(10):2030029. https://doi.org/10.1142/S0218127420300293
Cagin E, Chen DY, Siddiqui JJ, et al., 2007. Hysteretic metal-ferroelectric-semiconductor capacitors based on PZT/ZnO heterostructures. J Phys D Appl Phys, 40(8):2430–2434. https://doi.org/10.1088/0022-3727/40/8/003
Chang H, Li YX, Chen GR, et al., 2020. Extreme multistability and complex dynamics of a memristor-based chaotic system. Int J Bifurc Chaos, 30(8):2030019. https://doi.org/10.1142/S0218127420300190
Chen M, Feng Y, Bao H, et al., 2018. State variable mapping method for studying initial-dependent dynamics in memristive hyper-jerk system with line equilibrium. Chaos Sol Fract, 115:313–324. https://doi.org/10.1016/j.chaos.2018.07.025
Chen M, Feng Y, Bao H, et al., 2019a. Hybrid state variable incremental integral for reconstructing extreme multistability in memristive jerk system with cubic nonlinearity. Complexity, 2019:8549472. https://doi.org/10.1155/2019/8549472
Chen M, Ren X, Wu HG, et al., 2019b. Periodically varied initial offset boosting behaviors in a memristive system with cosine memductance. Front Inform Technol Electron Eng, 20(12):1706–1716. https://doi.org/10.1631/FITEE.1900360
Chen M, Ren X, Wu HG, et al., 2020. Interpreting initial offset boosting via reconstitution in integral domain. Chaos Sol Fract, 131:109544. https://doi.org/10.1016/j.chaos.2019.109544
Driscoll T, Kim HT, Chae BG, et al., 2009. Memory metamaterials. Science, 325(5947):1518–1521. https://doi.org/10.1126/science.1176580
Khorashadizadeh S, Majidi MH, 2018. Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications. Front Inform Technol Electron Eng, 19(9):1180–1190. https://doi.org/10.1631/FITEE.1601814
Kingni ST, Rajagopal K, Çiçek S, et al., 2020. Dynamic analysis, FPGA implementation, and cryptographic application of an autonomous 5D chaotic system with offset boosting. Front Inform Technol Electron Eng, 21(6):950–961. https://doi.org/10.1631/FITEE.1900167
Lai QX, Zhang L, Li ZY, et al., 2009. Analog memory capacitor based on field-configurable ion-doped polymers. Appl Phys Lett, 95(21):213503. https://doi.org/10.1063/1.3268433
Li CB, Sprott JC, 2016. Variable-boostable chaotic flows. Optik, 127(22):10389–10398. https://doi.org/10.1016/j.ijleo.2016.08.046
Li CB, Thio WJC, Iu HHC, et al., 2018. A memristive chaotic oscillator with increasing amplitude and frequency. IEEE Access, 6:12945–12950. https://doi.org/10.1109/ACCESS.2017.2788408
Liu RX, Dong RX, Qin SC, et al., 2020. A new type artificial synapse based on the organic copolymer memcapacitor. Org Electron, 81:105680. https://doi.org/10.1016/j.orgel.2020.105680
Ma XJ, Mou J, Liu J, et al., 2020. A novel simple chaotic circuit based on memristor-memcapacitor. Nonl Dynam, 100(3):2859–2876. https://doi.org/10.1007/s11071-020-05601-x
Martinez-Rincon J, Pershin YV, 2011. Bistable nonvolatile elastic-membrane memcapacitor exhibiting a chaotic behavior. IEEE Trans Electron Dev, 58(6):1809–1812. https://doi.org/10.1109/TED.2011.2126022
Martinez-Rincon J, di Ventra M, Pershin YV, 2010. Solid-state memcapacitive system with negative and diverging capacitance. Phys Rev B, 81(19):195430. https://doi.org/10.1103/PhysRevB.81.195430
Najem JS, Hasan MS, Williams RS, et al., 2019. Dynamical nonlinear memory capacitance in biomimetic membranes. Nat Commun, 10:3239. https://doi.org/10.1038/s41467-019-11223-8
Pershin YV, Ventra MD, 2011. Memory effects in complex materials and nanoscale systems. Adv Phys, 60(2):145–227. https://doi.org/10.1080/00018732.2010.544961
Pershin YV, Traversa FL, di Ventra M, 2015. Memcomputing with membrane memcapacitive systems. Nanotechnology, 26(22):225201. https://doi.org/10.1088/0957-4484/26/22/225201
Pham VT, Akgul A, Volos C, et al., 2017. Dynamics and circuit realization of a no-equilibrium chaotic system with a boostable variable. AEU-Int J Electron Commun, 78:134–140. https://doi.org/10.1016/j.aeue.2017.05.034
Pisarchik AN, Feudel U, 2014. Control of multistability. Phys Rep, 540(4):167–218. https://doi.org/10.1016/j.physRep2014.02.007
Rajagopal K, Akgul A, Jafari S, et al., 2018a. A chaotic memcapacitor oscillator with two unstable equilibriums and its fractional form with engineering applications. Nonl Dynam, 91(2):957–974. https://doi.org/10.1007/s11071-017-3921-3
Rajagopal K, Jafari S, Karthikeyan A, et al., 2018b. Hyper-chaotic memcapacitor oscillator with infinite equilibria and coexisting attractors. Circ Syst Signal Process, 37(9): 3702–3724. https://doi.org/10.1007/s00034-018-0750-7
Sun JW, Han GY, Wang YF, 2020. Dynamical analysis of memcapacitor chaotic system and its image encryption application. Int J Contr Autom Syst, 18(5):1242–1249. https://doi.org/10.1007/s12555-019-0015-7
Wang GY, Cai BZ, Jin PP, et al., 2016. Memcapacitor model and its application in a chaotic oscillator. Chin Phys B, 25(1):010503. https://doi.org/10.1088/1674-1056/25/1/010503
Wang GY, Shi CB, Wang XW, et al., 2017a. Coexisting oscillation and extreme multistability for a memcapacitor-based circuit. Math Probl Eng, 2017:6504969. https://doi.org/10.1155/2017/6504969
Wang GY, Zang SC, Wang XY, et al., 2017b. Memcapacitor model and its application in chaotic oscillator with memristor. Chaos, 27(1):013110. https://doi.org/10.1063/1.4973238
Wang XY, Yu J, Jin CX, et al., 2019. Chaotic oscillator based on memcapacitor and meminductor. Nonl Dynam, 96(1): 161–173. https://doi.org/10.1007/s11071-019-04781-5
Wang Z, Akgul A, Pham VT, et al., 2017. Chaos-based application of a novel no-equilibrium chaotic system with coexisting attractors. Nonl Dynam, 89(3):1877–1887. https://doi.org/10.1007/s11071-017-3558-2
Wu HG, Ye Y, Bao BC, et al., 2019a. Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system. Chaos Sol Fract, 121:178–185. https://doi.org/10.1016/j.chaos.2019.03.005
Wu HG, Ye Y, Chen M, et al., 2019b. Periodically switched memristor initial boosting behaviors in memristive hypogenetic jerk system. IEEE Access, 7:145022–145029. https://doi.org/10.1109/ACCESS.2019.2945754
Xu Q, Lin Y, Bao BC, et al., 2016. Multiple attractors in a non-ideal active voltage-controlled memristor based Chua’s circuit. Chaos Sol Fract, 83:186–200. https://doi.org/10.1016/j.chaos.2015.12.007
Xu Q, Tan X, Zhang YZ, et al., 2020. Riddled attraction basin and multistability in three-element-based memristive circuit. Complexity, 2020:4624792. https://doi.org/10.1155/2020/4624792
Yang LB, Yang QG, Chen GR, 2020. Hidden attractors, singularly degenerate heteroclinic orbits, multistability and physical realization of a new 6D hyperchaotic system. Commun Nonl Sci Numer Simul, 90:105362. https://doi.org/10.1016/j.cnsns.2020.105362
Yuan F, Li YX, 2019. A chaotic circuit constructed by a memristor, a memcapacitor and a meminductor. Chaos, 29(10):101101. https://doi.org/10.1063/1.5125673
Yuan F, Wang GY, Shen YR, et al., 2016. Coexisting attractors in a memcapacitor-based chaotic oscillator. Nonl Dynam, 86(1):37–50. https://doi.org/10.1007/s11071-016-2870-6
Yuan F, Deng Y, Li YX, et al., 2019a. The amplitude, frequency and parameter space boosting in a memristor-meminductor-based circuit. Nonl Dynam, 96(1):389–405. https://doi.org/10.1007/s11071-019-04795-z
Yuan F, Li YX, Wang GY, et al., 2019b. Complex dynamics in a memcapacitor-based circuit. Entropy, 21(2):188. https://doi.org/10.3390/e21020188
Zhang S, Zeng YC, Li ZJ, et al., 2018. Hidden extreme multi-stability, antimonotonicity and offset boosting control in a novel fractional-order hyperchaotic system without equilibrium. Int J Bifurc Chaos, 28(13):1850167. https://doi.org/10.1142/S0218127418501675
Zhang YZ, Liu Z, Wu HG, et al., 2019. Extreme multistability in memristive hyper-jerk system and stability mechanism analysis using dimensionality reduction model. Eur Phys J Spec Top, 228(10):1995–2009. https://doi.org/10.1140/epjst/e2019-800238-0
Zhao L, Fan Z, Cheng SL, et al., 2020. An artificial optoelectronic synapse based on a photoelectric memcapacitor. Adv Electron Mater, 6(2):1900858. https://doi.org/10.1002/aelm.201900858
Zhou W, Wang GY, Iu HHC, et al., 2020. Complex dynamics of a non-volatile memcapacitor-aided hyperchaotic oscillator. Nonl Dynam, 100(4):3937–3957. https://doi.org/10.1007/s11071-020-05722-3
Zhou Z, Yu DS, Wang XY, 2017. Investigation on the dynamic behaviors of the coupled memcapacitor-based circuits. Chin Phys B, 26(12):120701. https://doi.org/10.1088/1674-1056/26/12/120701
Author information
Authors and Affiliations
Contributions
Bocheng BAO designed the research. Bei CHEN and Quan XU processed the data. Bei CHEN drafted the paper. Quan XU and Mo CHEN helped organize the paper. Huagan WU and Bocheng BAO revised and finalized the paper.
Corresponding author
Ethics declarations
Bei CHEN, Quan XU, Mo CHEN, Huagan WU, and Bocheng BAO declare that they have no conflict of interest.
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 51777016 and 61801054), the Natural Science Foundation of Jiangsu Province, China (No. BK20191451), the Natural Science Foundation of Changzhou, Jiangsu Province, China (No. CJ20190037), and the Open Research Fund of Key Laboratory of MEMS of Ministry of Education, Southeast University, China
Rights and permissions
About this article
Cite this article
Chen, B., Xu, Q., Chen, M. et al. Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator. Front Inform Technol Electron Eng 22, 1517–1531 (2021). https://doi.org/10.1631/FITEE.2000622
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.2000622