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Investigation of dynamical properties in hysteresis-based a simple chaotic waveform generator with two stable equilibrium

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  • Joshi, Manoj
  • Ranjan, Ashish

Abstract

This research article describes a novel simple chaotic oscillator using bistable operation to generate chaotic waveform. In this design, chaos generation uses differential hysteresis phenomena of an Operational Amplifier (Op-Amp) with tank circuit. The behavior of the proposed chaotic system is investigated in terms of basic dynamical characteristics viz. equilibrium point stability, divergence, Lyapunov exponents, influence of initial condition, routes of chaos, basin of attraction and phase portraits by using theoretical analysis in MATLAB. We observed that proposed chaotic system belongs to the class of hidden attractor with two stable equilibrium points without quadratic or multiplying term that reduced the circuit complexity. Finally, an experimental investigation of the proposed design is performed that validates the theoretical and PSPICE results.

Suggested Citation

  • Joshi, Manoj & Ranjan, Ashish, 2020. "Investigation of dynamical properties in hysteresis-based a simple chaotic waveform generator with two stable equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920300953
    DOI: 10.1016/j.chaos.2020.109693
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    References listed on IDEAS

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    1. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    2. Jafari, Sajad & Dehghan, Soroush & Chen, Guanrong & Kingni, Sifeu Takougang & Rajagopal, Karthikeyan, 2018. "Twin birds inside and outside the cage," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 135-140.
    3. Han, Fengling & Lü, Jinhu & Yu, Xinghuo & Chen, Guanrong, 2006. "Dynamical behaviours of a 3D hysteresis-based system," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 182-192.
    4. Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Khalaf, Abdul Jalil M. & Alsaedi, Ahmed & Pham, Viet-Thanh & Hayat, Tasawar, 2018. "Investigation of dynamical properties in a chaotic flow with one unstable equilibrium: Circuit design and entropy analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 7-13.
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    Cited by:

    1. Manoj Joshi & Vivek Bhatt & Ashish Ranjan, 2023. "A single parametrically controlled megastable multiscroll attractor with an unstable node," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(5), pages 1-9, May.
    2. Qifeng Fu & Xuemei Xu & Chuwen Xiao, 2022. "LQR Chaos Synchronization for a Novel Memristor-Based Hyperchaotic Oscillator," Mathematics, MDPI, vol. 11(1), pages 1-16, December.

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