Abstract
This research article contributes a Chua’s diode implementation using a modern active block Current Controlled Current Conveyor Transconductance Amplifier (CCCCTA) with an active MOS transistor for electronically tunable feature. CCCCTA and MOS resistor are responsible for the variation in Chua’s diode characteristics and their performance is well studied with the help of dynamical aspects like dissipativity, invariance, bifurcation diagram, Lyapunov exponents, and basin of attraction. The proposed model has a hidden attractor with one unstable node equilibrium and two symmetric stable node equilibrium points. In addition to numerical simulation in MATLAB, the electronic circuit for the proposed Chua’s circuit is successfully verified in PSPICE and hardware implementation using commercially available ICs (AD844, CA3080). Chua’s traditional chaotic response (double scroll, Rossler, and large limit cycle) can be easily observed by: (i) adjusting the coupling resistor between two capacitor present in a Chua’s circuit, (ii) tuning the bias current of CCCCTA present in the proposed Chua’s diode, and (iii) by tuning the controlling voltage of MOS resistor (RMOS). The feasibility of the proposed work applies to Chaotic Amplitude Shift Keying (CASK) transmission. Finally, a comparative study is studied with the existing works of literature.
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References
B.C. Bao, Q.D. Li, N. Wang, Q. Xu, Multistability in Chua’s circuit with two stable node-foci Chaos. Interdisciplin. J. Nonlinear Sci. 26(4), 043111 (2016)
V. Bhatt, A. Ranjan, Y.S. Singh, Resistorless Chua’s diode implementation for Chaotic oscillation employing single EXCCCII. AEU-Int. J. Electron. Commun. 156, 154398 (2022)
H.P. Chen, Y.S. Hwang, Y.T. Ku, Voltage-mode and current-mode resistorless third-order quadrature oscillator. Appl. Sci. 7(2), 179 (2017)
M. Chen, X. Quan, B. Bao, Hidden attractors in a practical Chua’s circuit based on a modified Chua’s diode. Electronics Letter 52(1), 23–25 (2015)
C.K. Choubey, S.K. Paul, Implementation of Chaotic oscillator by designing a simple Chua’s diode using a single VDTA. Int. J. Electron. Commun. 124, 153360 (2020)
L.O. Chua, M. Komuro, T. Matsumoto, The double scroll family. IEEE Trans. Circ. Syst. 33(11), 1073–1118 (1986)
E.T. Cuautle, A.G. Hernndez, Implementation of a chaotic oscillator by designing Chua’s diode with CMOS CFOAs. Analog Integr. Circ. Sig. Process 48(2), 159–162 (2006)
G. Gandhi, An improved Chua’s circuit and its use in hyper chaotic circuit. Analog Int. Circ. Signal Process. 46(2), 173–178 (2006)
P. Gaspard, Rossler systems. New York: Routledge (1st ed.), 808–814 (2005).
K. Gopakumar, B. Premlet, K.G. Gopchandran, Implementation of Chua’s circuit usingsimulated inductance. Int. J. Electron. 98(5), 667–677 (2011)
S. Jafari, A. Ahmadi, A.J.M. Khalaf, H.R. Abdolmohammadi, V.T. Pham, F.E. Alsaadi, A new hidden Chaotic attractor with extreme multi-stability. AEU – Int J. Electro. Commun. 89, 131–135 (2018)
M.D. Johansyah, A new 3-D multistable Chaotic system with line equilibrium: dynamic analysis and synchronization. Int. J. Quant. Res. Model. 2(1), 55–66 (2021)
M. Joshi, A. Ranjan, Investigation of dynamical properties in hysteresis-based a simple chaotic waveform generator with two stable equilibrium. Chaos Solitons Fractals 134, 109693 (2020)
M. Joshi, P. Mohit, A. Ranjan, N-th-order simple hyperjerk system with unstable equilibrium and its application as RPG. Circ. Syst. Signal Process. 40, 5913–5934 (2021)
M.P. Kennedy, Robust op-amp realization of Chua’s circuit. Frequenz 46, 66–80 (1992)
R. Kılıç, U. Cam, H. Kuntman, E. Uzunhisarcıklı, Realization of inductorless Chua’s circuit using FTFN-based nonlinear resistor and inductance simulator. Frequenz 58, 1–2 (2004)
N. Kumar, J. Vista, A. Ranjan, A tuneable active inductor employing DXCCTA: grounded and floating operation. Microelectron. J. 90, 1–11 (2019)
A.K. Kushwaha, S.K. Paul, Inductorless realization of Chua’s oscillator using DVCCTA. Analog Integr. Circ. Sig. Process 88(1), 137–150 (2016)
A.K. Kushwaha, S.K. Paul, Chua’s oscillator using operational transresistance amplifier. Rev. Roum. Sci. Techn. Électrotechn. Et Énerg. 61(3), 299–303 (2016)
G.A. Leonov, N.V. Kuznetsov, V.I. Vagaitsev, Localization of hidden Chuaʼs attractors. Phys. Lett. A 375(23), 2230–2233 (2011)
T. Liu, H. Yan, S. Banerjee, J. Mou, A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation. Chaos Solitons Fractals 145, 110791 (2021)
E.N. Lorenz, Deterministic non-periodic flow simple 4d chaotic oscillator. J. Atmos. Sci. 20, 130–141 (1963)
A. Mishra, K. Sehra, S. Sahil, A. Joshi, P. Kasturi, M. Saxena, Memristor based cryptographic information processing for secured communication systems. In: 5th International Conference on Devices, Circuits and Systems (ICDCS), IEEE, Coimbatore, India, 167–171 (2020).
O. Morgul, Inductorless realization of Chua oscillator. Electronics Letter 31(17), 1403–1404 (1995)
L.N. Nguenjou, G. Kom, J.R.M. Pone, K. Jacques, A. Tiedeu, A window of multistability in Genesio-Tesi chaotic system, synchronization and application for securing information. AEU Int. J. Electron. Commun. 99, 201–214 (2019)
V.T. Pham, C. Volos, S. Jafari, T. Kapitaniak, Coexistence of hidden Chaotic attractors in a novel no-equilibrium system. Nonlinear Dyn. 87(3), 2001–2010 (2017)
V.T. Pham, S. Jafari, C. Volos, T. Kapitaniak, Different families of hidden attractors in a new chaotic system with variable equilibrium. Int. J. Bifurcation Chaos 27(9), 1750138 (2017)
N. Pratyusha, S. Mandal, Design and Implementation of a Novel Circuit-Based Memristive Non-autonomous Hyperchaotic System with Conservative and Offset Boosting for Applications to Image Encryption. Circuits, Systems, and Signal Processing, 1–23 (2023).
R. Senani, S. Gupta, Implementation of Chua’s chaotic circuit using current feedback opamp. Electronics Letter 34(9), 829–830 (1998)
M. Siripruchyanun, P. Silapan, W. Jaikla, Realizatio of CMOS current controlled current convey or transconductance amplifier and its application. J. Active Passive Dev. 4, 35–53 (2009)
M. Siripruchyanun, W. Jaikla, Current controlled current conveyor transconductance amplifier (CCCCTA): a building block for analog signal processing. Electr. Eng. 90(6), 443–453 (2008)
J.C. Sprott, A new chaotic jerk circuit. IEEE Trans. Circuits Syst. II(58), 240–243 (2011)
N.V. Stankevich, N.V. Kuznetsov, G.A. Leonov, L.O. Chua, Scenario of the birth of hidden attractors in the Chua circuit. Int. J. Bifurcation Chaos 27(12), 1730038 (2017)
L.A.B. Torres, L.A. Aguirre, Inductorless Chua’s circuit. Electronics Lett. 36(23), 1915–1916 (2000)
N. Wang, G. Zhang, N.V. Kuznetsov, H. Bao, Hidden attractors and multistability in a modified Chua’s circuit. Commun. Nonlinear Sci. Numer. Simul. 92, 1–22 (2020)
A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Determining Lyapunov exponents from a time series. Physica D 16(3), 285–317 (1985)
S. Zhang, C. Li, J. Zheng, X. Wang, Z. Zeng, X. Peng, Generating any number of initial offset-boosted coexisting chua’s double-scroll attractors via piecewise-nonlinear memristor. IEEE Trans. Industr. Electron. 69(7), 7202–7212 (2021)
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Bhatt, V., Ranjan, A. & Joshi, M. CCCCTA-based Chua’s Circuit for Chaotic Oscillation. Circuits Syst Signal Process 43, 2051–2072 (2024). https://doi.org/10.1007/s00034-023-02579-w
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DOI: https://doi.org/10.1007/s00034-023-02579-w