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Chaos in a novel Wien bridge-based RC chaotic oscillator: dynamic analysis with application to image encryption

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Abstract

In the present contribution, we design a novel chaotic circuit with a symmetrical nonlinear component by replacing the single semiconductor diode in the original circuit by [Namajunas & Tamasevicius, 1995] with a pair of diodes connected in antiparallel. By exploiting the Shockley diode equation and adopting a judicious choice of state variables, we derive a smooth (i.e. with hyperbolic nonlinearities) mathematical model to investigate both the regular and chaotic dynamics of the novel RC oscillator. In addition to the familiar period-doubling bifurcations already observed in previous versions of the same oscillator, the novel oscillator exhibits more interesting dynamical properties including for instance, symmetry breaking bifurcation, merging crisis and coexisting multiple attractors as well. Interestingly, one of the most gratifying (and rare) features of the new circuit is the occurrence of both bubbles and reverse bubbles of bifurcation for some suitable parameter ranges. An excellent agreement is observed between theoretical and experimental results. The model is digitalized for digital image encryption. First the Hahn orthogonal moments of each pixel of the plain image is computed, and then Knuth permutation algorithm is combined to chaotic sequences to scramble the resulting image in the transform domain. Finally, the permuted image will be diffused using the pseudo random chaotic sequences. Security analysis indicates good performances of the model to encrypt and decrypt digital images.

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Funding

This work is partially funded by Centre for Nonlinear Systems, Chennai Institute of Technology, India vide funding number CIT/CNS/2021/RD/022.

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Authors and Affiliations

  1. Center for Artificial Intelligence, Chennai Institute of Technology, Chennai, India

    Janarthanan Ramadoss & Jacques Kengne

  2. College of Technology, The University of Buea, Buea, Cameroon

    Adelaide Nicole Kengnou Telem

  3. Laboratoire d’Automatique Et Informatique Appliquée (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon

    Jacques Kengne, Adelaide Nicole Kengnou Telem & Nestor Tsafack

  4. Laboratory of Electronics and Signal Processing, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Jacques Kengne & Nestor Tsafack

  5. Research Unit of Laboratory of Energy and Artificial Intelligence (RU-LEAI), Electrical Engineering Department of ISTAMA, University of Douala, P.O. Box 3223, Douala, Cameroon

    Nestor Tsafack

  6. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, India

    Karthikeyan Rajagopal

  7. Department of Electronics and Communications Engineering and University Centre for Research & Development, Chandigarh University, Mohali, 140413, Punjab, India

    Karthikeyan Rajagopal

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  1. Janarthanan Ramadoss
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  2. Jacques Kengne
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  3. Adelaide Nicole Kengnou Telem
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  5. Karthikeyan Rajagopal
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Correspondence to Jacques Kengne.

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Ramadoss, J., Kengne, J., Telem, A.N.K. et al. Chaos in a novel Wien bridge-based RC chaotic oscillator: dynamic analysis with application to image encryption. Analog Integr Circ Sig Process 112, 495–516 (2022). https://doi.org/10.1007/s10470-022-02061-8

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