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Hidden Attractor in a Asymmetrical Novel Hyperchaotic System Involved in a Bounded Function of Exponential Form with Image Encryption Application

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Intelligent Data Engineering and Analytics (FICTA 2023)

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 371))

Abstract

In this paper, an asymmetrical novel 4D system with a bounded function of exponential form, which can exhibit chaotic and hyperchoatic behaviors has been proposed. By calculating Lyapunov exponents and bifurcation diagram, the dynamical behaviors of such system are discovered. The proposed system has involved in bounded function and we show the behavior changes according to the corresponding function. An application to image encryption has been obtained.

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References

  1. Sooraksa, P., Chen, G.: Chen system as a controlled weather model-physical principle, engineering design and real applications. Int. J. Bifu. Chaos 28, 1–12 (2018)

    MathSciNet  Google Scholar 

  2. Udaltsov, V.S., Goedgebuer, J.P., Larger, L., Cuenot, J.B., Levy, P., Rhodes, W.T.: Communicating with hyperchaos: the dynamics of a DNLF emitter and recovery of transmitted information. Opt. Spectrosc. 95, 114–118 (2003)

    Article  Google Scholar 

  3. Schiff, S.J., Jerger, K., Duong, D.H., Chang, T., Spano, M.L., Ditto, W.L.: Controlling chaos in the brain. Nature 370, 615–620 (1994)

    Article  Google Scholar 

  4. Lorenz, E.N.: Deterministic nonperiodic flow. Atmos. Sci. 20, 130–141 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lorenz, E.: On the prevalence of aperiodicity in simple systems. In: Grmela, M., Marsden, J.E. (eds.) Global Analysis, Lecture Notes in Mathematics, 755, pp. 53–75. Springer, Berlin

    Google Scholar 

  6. Chua, L., Komuro, M., Matsumoto, T.: The double scroll family. IEEE Trans. Circuits Syst. 33, 1073–1118 (1986)

    Article  MATH  Google Scholar 

  7. Chen, G.R., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurc. Chaos 9, 1465–1466 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lu, J.H., Chen, G.: A new chaotic attractor coined. Int. J. Bifurc. Chaos 12, 659–661 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wei, Z., Yang, Q.: Dynamical analysis of a new autonomous 3-D chaotic system only with stable equilibria. Nonlin. Anal. Real World Appl. 12, 106–118 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Yang, Q., Wei, Z., Chen, G.: An unusual 3D autonomous quadratic chaotic system with two stable node-foci. Int. J. Bifurc. Chaos 20, 1061–1083 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kuznetsov, N.V.: The Lyapunov dimension and its estimation via the Leonov method. Phys. Lett. A 380(25–26), 2142–2149 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kuznetsov, N.V.: The Lyapunov dimension and its estimation via the Leonov method. Phys. Lett. A 380(25–26), 2142–2149 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rossler, O.E.: An equation for hyperchaos. Phys. Lett. A 71, 155–157 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  14. Barboza, R.: Dynamics of a hyperchoatic Lorenz system. Int. J. Bifurc. Chaos 17, 4285 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Neimark, Y., Shilnikov, L.: A condition for the generation of periodic motions SOV. Math. Docklady 6(163), 1261–1264 (1965)

    Google Scholar 

  16. Kuznetsov, N.V.: The Lyapunov dimension and its estimation via the Leonov method. Phys. Lett. A 380(25–26), 2142–2149 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. Leonov, G.A., Kuznetsov, N.V.: Hidden attractors in dynamical systems. From hidden oscillation in Hilbert Kolmogrov, Aizerman, and Kalman problems to hidden chaotic attractor in chua circuits. Int. J. Bifurc. Chaos 23, 1–69

    Google Scholar 

  18. Hua, Z., Zhou, Z.: Design of image cipher using block-based scrambling and image filtering. Inf. Sci. 396, 97–113 (2017)

    Article  MATH  Google Scholar 

  19. Souyah, A., Faraoun, K.M.: Fast and efficient randomized encryption scheme for digital images based on quadtree decomposition and reversible memory cellular automate. Nonlin. Dyn. 84, 715–732 (2016)

    Google Scholar 

  20. Nestor, T., Belazi, A., Abd-El-Atty, B., Aslam, Md., Volos, C., De Dieu, N., El-Latif, A.: A new 4D hyperchaotic system with dynamics analysis, synchronization, and application to image encryption. Symmetry 14, 424 (2022)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Computer Science and Mathematics, University of Kufa, Kufa, Iraq

    Ali A. Shukur

  2. Faculty of Mechanics-Mathematics, Belarusian State University, Minsk, Belarus

    Ali A. Shukur

  3. National University of Malaysia, Kuala Lampur, Malaysia

    Mohanad A. AlFallooji

Authors
  1. Ali A. Shukur
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  2. Mohanad A. AlFallooji
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Corresponding author

Correspondence to Ali A. Shukur .

Editor information

Editors and Affiliations

  1. Department of Electronics Engineering, Faculty of Engineering and Technology (UNSIET), Veer Bahadur Singh Purvanchal University, Jaunpur, Uttar Pradesh, India

    Vikrant Bhateja

  2. Cardiff School of Technologies, Cardiff Metropolitan University, Cardiff, Warwickshire, UK

    Fiona Carroll

  3. Faculty of Engineering, University of Porto, Porto, Portugal

    João Manuel R. S. Tavares

  4. Cardiff Metropolitan University, Cardiff, Warwickshire, UK

    Sandeep Singh Sengar

  5. Faculty of Computer and Information Science, University of Ljubljana, Ljubljana, Slovenia

    Peter Peer

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© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Shukur, A.A., AlFallooji, M.A. (2023). Hidden Attractor in a Asymmetrical Novel Hyperchaotic System Involved in a Bounded Function of Exponential Form with Image Encryption Application. In: Bhateja, V., Carroll, F., Tavares, J.M.R.S., Sengar, S.S., Peer, P. (eds) Intelligent Data Engineering and Analytics. FICTA 2023. Smart Innovation, Systems and Technologies, vol 371. Springer, Singapore. https://doi.org/10.1007/978-981-99-6706-3_37

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