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A New 3D Chaotic System with only Quadratic Nonlinearities: Analysis and Circuit Implantation

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Chaotic Systems with Multistability and Hidden Attractors

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 40))

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Abstract

Chaos is an interesting nonlinear behavior of many natural and artificial systems. Many researchers are studying chaos theory and chaotic systems, and various applications of chaos have been introduced in such as biological systems, communications, information encryption, electronic circuits, lasers, etc.

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References

  1. H. Gao, Y. Zhang, S. Liang, D. Li, A new chaotic algorithm for image encryption. Chaos, Solitons Fractals 29(2), 393–399 (2006)

    Article  Google Scholar 

  2. M.J. Ogorzalek, Chaos and Complexity in Nonlinear Electronic Circuits (World Scientific, Singapore, 1997)

    Book  Google Scholar 

  3. C.K. Volos, I.M. Kyprianidis, I.N. Stouboulos, Image encryption process based on chaotic synchronization phenomena. Signal Process. 93(5), 1328–1340 (2013)

    Article  Google Scholar 

  4. V.-T. Pham, S. Jafari, C. Volos, A. Giakoumis, S. Vaidyanathan, T. Kapitaniak, A chaotic system with equilibria located on the rounded square loop and its circuit implementation. IEEE Trans. Circuits Syst. II Express Briefs 63(9), 878–882 (2016)

    Article  Google Scholar 

  5. J. Chen, X. Zhang, J. Peng, Time-delayed chaotic circuit design using all-pass filter. IEEE Trans. Circuits Syst. I Regul. Pap. 61(10), 2897–2903 (2014)

    Article  MathSciNet  Google Scholar 

  6. C. Shen, S. Yu, J. Lü, G. Chen, A systematic methodology for constructing hyperchaotic systems with multiple positive lyapunov exponents and circuit implementation. IEEE Trans. Circuits Syst. I Regul. Pap. 61(3), 854–864 (2014)

    Article  Google Scholar 

  7. V.-T. Pham, S. Vaidyanathan, C. Volos, S. Jafari, S.T. Kingni, A no-equilibrium hyperchaotic system with a cubic nonlinear term. Optik: Int. J. Light Electron Opt. 127(6), 3259–3265 (2016)

    Google Scholar 

  8. F.R. Tahir, S. Jafari, V.-T. Pham, C. Volos, X. Wang, A novel no-equilibrium chaotic system with multiwing butterfly attractors. International Journal of Bifurcation and Chaos 25(04), 1550056 (2015)

    Article  MathSciNet  Google Scholar 

  9. V.-T. Pham, C. Volos, S. Jafari, X. Wang, Generating a novel hyperchaotic system out of equilibrium. Optoelectronics and Advanced Materieals: Rapid Communication 8(5–6), 535–539 (2014)

    Google Scholar 

  10. V.-T. Pham, C. Volos, S. Jafari, Z. Wei, X. Wang, Constructing a novel no-equilibrium chaotic system. Int. J. Bifurc. Chaos 24(05), 1450073 (2014)

    Article  MathSciNet  Google Scholar 

  11. G. Leonov, N. Kuznetsov, V. Vagaitsev, Localization of hidden chua’s attractors. Phys. Lett. A 375(23), 2230–2233 (2011)

    Article  MathSciNet  Google Scholar 

  12. G. Leonov, N. Kuznetsov, V. Vagaitsev, Hidden attractor in smooth Chua systems. Physica D 241(18), 1482–1486 (2012)

    Article  MathSciNet  Google Scholar 

  13. G.A. Leonov, N.V. Kuznetsov, Hidden attractors in dynamical systems. from hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits. Int. J. Bifurc. Chaos 23(1), 1330002 (2013)

    Google Scholar 

  14. G. Leonov, N. Kuznetsov, M. Kiseleva, E. Solovyeva, A. Zaretskiy, Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor. Nonlinear Dyn. 77(1–2), 277–288 (2014)

    Article  Google Scholar 

  15. G. Leonov, N. Kuznetsov, T. Mokaev, Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity. Commun. Nonlinear Sci. Numer. Simul. 28(1), 166–174 (2015)

    Article  MathSciNet  Google Scholar 

  16. G. Leonov, N. Kuznetsov, T. Mokaev, Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion. Eur. Phys. Jo.: Special Topics 224(8), 1421–1458 (2015)

    Google Scholar 

  17. P. Sharma, M. Shrimali, A. Prasad, N. Kuznetsov, G. Leonov, Control of multistability in hidden attractors. Eur. Phys. J.: Special Topics 224(8), 1485–1491 (2015)

    Google Scholar 

  18. P.R. Sharma, M.D. Shrimali, A. Prasad, N.V. Kuznetsov, G.A. Leonov, Controlling dynamics of hidden attractors. Int. J. Bifurc. Chaos 25(04), 1550061 (2015)

    Article  MathSciNet  Google Scholar 

  19. S. Jafari, J. Sprott, S.M.R.H. Golpayegani, Elementary quadratic chaotic flows with no equilibria. Phys. Lett. A 377(9), 699–702 (2013)

    Article  MathSciNet  Google Scholar 

  20. S. Jafari, J.C. Sprott, V.-T. Pham, S.M.R.H. Golpayegani, A.H. Jafari, A new cost function for parameter estimation of chaotic systems using return maps as fingerprints. Int. J. Bifurc. Chaos 24(10), 1450134 (2014)

    Article  MathSciNet  Google Scholar 

  21. S. Jafari, V.-T. Pham, T. Kapitaniak, Multiscroll chaotic sea obtained from a simple 3d system without equilibrium. Int. J. Bifurc. Chaos 26(02), 1650031 (2016)

    Article  MathSciNet  Google Scholar 

  22. V.-T. Pham, S. Vaidyanathan, C. Volos, S. Jafari, N. Kuznetsov, T. Hoang, A novel memristive time-delay chaotic system without equilibrium points. Eur. Phys. J.: Special Topics 225(1), 127–136 (2016)

    Google Scholar 

  23. Z. Wei, Dynamical behaviors of a chaotic system with no equilibria. Phys. Lett. A 376(2), 102–108 (2011)

    Article  MathSciNet  Google Scholar 

  24. X. Wang, G. Chen, Constructing a chaotic system with any number of equilibria. Nonlinear Dyn. 71(3), 429–436 (2013)

    Article  MathSciNet  Google Scholar 

  25. M. Molaie, S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, Simple chaotic flows with one stable equilibrium. Int. J. Bifurc. Chaos 23(11), 1350188 (2013)

    Article  MathSciNet  Google Scholar 

  26. S. Kingni, S. Jafari, H. Simo, P. Woafo, Three-dimensional chaotic autonomous system with only one stable equilibrium: Analysis, circuit design, parameter estimation, control, synchronization and its fractional-order form. Eur. Phys. J. Plus 129(5), 1–16 (2014)

    Article  Google Scholar 

  27. S.-K. Lao, Y. Shekofteh, S. Jafari, J.C. Sprott, Cost function based on Gaussian mixture model for parameter estimation of a chaotic circuit with a hidden attractor. Int. J. Bifurc. Chaos 24(01), 1450010 (2014)

    Article  MathSciNet  Google Scholar 

  28. V.-T. Pham, C. Volos, S. Jafari, X. Wang, Generating a novel hyperchaotic system out of equilibrium. Optoelectronics and Advanced Materiels: Rapid Communication 8(5–6), 535–539 (2014)

    Google Scholar 

  29. S. Jafari, J. Sprott, Simple chaotic flows with a line equilibrium. Chaos, Solitons Fractals 57, 79–84 (2013)

    Article  MathSciNet  Google Scholar 

  30. S.T. Kingni, V.-T. Pham, S. Jafari, G.R. Kol, P. Woafo, Three-dimensional chaotic autonomous system with a circular equilibrium: Analysis, circuit implementation and its fractional-order form. Circuits Systems Signal Process. 35(6), 1933–1948 (2016)

    Article  MathSciNet  Google Scholar 

  31. V.-T. Pham, S. Jafari, C. Volos, S. Vaidyanathan, T. Kapitaniak, A chaotic system with infinite equilibria located on a piecewise linear curve. Optik: Int. J. Light Electron Opt. 127(20), 9111–9117 (2016)

    Google Scholar 

  32. V.-T. Pham, S. Jafari, X. Wang, J. Ma, A chaotic system with different shapes of equilibria. Int. J. Bifurc. Chaos 26(04), 1650069 (2016)

    Article  MathSciNet  Google Scholar 

  33. T. Gotthans, J. Petržela, New class of chaotic systems with circular equilibrium. Nonlinear Dyn. 81(3), 1143–1149 (2015)

    Article  MathSciNet  Google Scholar 

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Correspondence to Seyede Sanaz Hosseini .

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Hosseini, S.S., Jafari, MA., Jafari, S., Pham, VT., Wang, X. (2021). A New 3D Chaotic System with only Quadratic Nonlinearities: Analysis and Circuit Implantation. In: Wang, X., Kuznetsov, N.V., Chen, G. (eds) Chaotic Systems with Multistability and Hidden Attractors. Emergence, Complexity and Computation, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-030-75821-9_24

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