A NOVEL S-BOX DESIGN ALGORITHM AND FUZZY-PID CONTROLLER DESIGN FOR A 5-D BURKE-SHAW SYSTEM WITH HIDDEN HYPERCHAOS

Qingxia Ma, Wenqiang Luo, Hadi Jahanshahi, Unal Cavusoglu, Akif Akgul, and Xianguang Lin

References

  1. [1] Sprott JC. Some simple chaotic flows. Phys Rev E 1994;50:647-650.
  2. [2] Šil’nikov LP. A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type. Math USSR-Sbornik 1970;10:91-102.
  3. [3] Silva CP. Shil’nikov’s theorem-a tutorial. IEEE Trans Circuits Syst I Fundam Theory Appl 1993;40:675-682.
  4. [4] Zhou T, Chen G. Classification of chaos in 3-D autonomous quadratic systems-I: basic framework and methods. Int J Bifurc Chaos 2006;16:2459-2479.
  5. [5] Feng L, Yinlai J. Hopf bifurcation analysis and numerical simulation in a 4D-hyoerchaotic system. Nonlinear Dyn 2012;67:2857-2864.
  6. [6] Nik HS, Van Gorder RA. Competitive modes for the Baier-Sahle hyperchaotic flow in arbitrary dimensions. Nonlinear Dyn 2013;74:581-590.
  7. [7] Chen Y, Yang Q. Dynamics of a hyperchaotic Lorenz-type system. Nonlinear Dyn 2014;77:569-81.
  8. [8] Hu G. Generating hyperchaotic attractors with three positive Lyapunov exponents via state feedback control. Int J Bifurc Chaos 2009;19:651-660.
  9. [9] Yang Q, Chen C. A 5D hyperchaotic system with three positive Lyapunov exponents coined. Int J Bifurc Chaos 2013;23:1350109.
  10. [10] Yang Q, Osman WM, Chen C. A new 6D hyperchaotic system with four positive Lyapunov exponents coined. Int J Bifurc Chaos 2015;25:1550060.
  11. [11] Leonov GA, Kuznetsov N V. 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 2013;23:1330002.
  12. [12] Leonov GA, Kuznetsov N V, Mokaev TN. Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity. Commun Nonlinear Sci Numer Simul 2015;28:166-174.
  13. [13] Kuznetsov N V, Leonov GA. Numerical Visualization of attractors: Self-exciting and hidden attractors. Handb Appl Chaos Theory 2016:135-143.
  14. [14] Leonov GA, Kuznetsov N V, Vagaitsev VI. Localization of hidden Chuaʼs attractors. Phys Lett A 2011;375:2230-2233.
  15. [15] Leonov GA, Kuznetsov N V, Vagaitsev VI. Hidden attractor in smooth Chua systems. Phys D Nonlinear Phenom 2012;241:1482-1486.
  16. [16] Z.C. Wei, Dynamical behaviors of a chaotic system with no equilibria, Physics Letters A, 376, 2011, 102-108.
  17. [17] Z.C. Wei, R.R. Wang, and A.P. Liu, A new finding of the existence of hidden hyperchaotic attractors with no equilibria, Mathematics and Computers in Simulation, 100, 2014, 13-23.
  18. [18] V.-T. Pham, C.Volos, S.Jafari, Z.C. Wei, and X. Wang, Constructing a novel no-equilibrium chaotic system, International Journal of Bifurcation and Chaos, 24, 2014, 1450073.
  19. [19] M. Molaie, S. Jafari, J. C. Sprott, and S. M. R. H. Golpayegani, Simple chaotic flows with one stable equilibrium, International Journal of Bifurcation and Chaos, 23, 2013, 1350188.
  20. [20] Z.C. Wei, W. Zhang, Z. Wang, and M.H. Yao, Hidden Attractors and Dynamical Behaviors in an Extended Rikitake System, International Journal of Bifurcation and Chaos, 25, 2015, 1550028.
  21. [21] Z. C. Wei, and I. Pehlivan, Chaos, coexisting attractors, and circuit design of the generalized Sprott C system with only two stable equilibria, Optoelectronics and Advanced Materials-Rapid Communications, 6, 2012, 742-745.
  22. [22] Z.C. Wei, I. Moroz, J.C. Sprott, A. Akgul, and W. Zhang, Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo, Chaos,, 27(3), 2017, 033101.
  23. [23] V.-T.Pham, S. Jafari, C. Volos, S. Vaidyanathan and T. Kapitaniak, A chaotic system with infinite equilibria located on a piecewise linear curve, Optik-International Journal for Light and Electron Optics, 127, 2016 9111-9117.
  24. [24] S. Jafari, J. C. Sprott, and M. Molaie, A simple chaotic flow with a plane of equilibria, International Journal of Bifurcation and Chaos, 26, 2016, 1650098.
  25. [25] S. Jafari, J. C. Sprott, V.-T.Pham, C. Volos, and C.B. Li, Simple chaotic 3D flows with surfaces of equilibria, Nonlinear Dynamics, 86, 2016, 1349-1358.
  26. [26] Li C, Akgul A, Sprott J.C, Iu H. C, Thio W.: A symmetric pair of hyperchaotic attractors. Int. J. Circ. Theor. Appl. 2018; 1-10, DOI: 10.1002/cta.2569.
  27. [27] Li C, Sprott J.C, Kapitaniak T, Lu T. Infinite lattice of hyperchaotic strange attractors, Chaos, Solitons & Fractals, 2018; 109: 76-82.
  28. [28] Wang Z, Cang S, Ochola EO, Sun Y. A hyperchaotic system without equilibrium. Nonlinear Dyn 2012;69:531-537.
  29. [29] Wei Z, Wang R, Liu A. A new finding of the existence of hidden hyperchaotic attractors with no equilibria. Math Comput Simul 2014;100:13-23.
  30. [30] Mahmoud GM, Mahmoud EE, Ahmed ME. On the hyperchaotic complex Lü system. Nonlinear Dyn 2009;58:725-738.
  31. [31] Wei Z, Yu P, Zhang W, Yao M. Study of hidden attractors, multiple limit cycles from Hopf bifurcation and boundedness of motion in the generalized hyperchaotic Rabinovich system. Nonlinear Dyn 2015;82:131-141.
  32. [32] Wei Z, Zhang W. Hidden hyperchaotic attractors in a modified Lorenz-Stenflo system with only one stable equilibrium. Int J Bifurc Chaos 2014;24:1450127.
  33. [33] Dudkowski D, Jafari S, Kapitaniak T, Kuznetsov N V, Leonov GA, Prasad A. Hidden attractors in dynamical systems. Phys Rep 2016;637:1-50.
  34. [34] Kapitaniak T, Leonov GA. Multistability: uncovering hidden attractors Eur Phys J-Spec Top 2015; 224 (8) :1405-1408
  35. [35] Pehlivan İ, Uyaroğlu Y. A new 3D chaotic system with golden proportion equilibria: Analysis and electronic circuit realization. Comput Electr Eng 2012;38:1777-1784.
  36. [36] Koyuncu I, Ozcerit AT, Pehlivan I. Implementation of FPGA-based real time novel chaotic oscillator. Nonlinear Dyn 2014;77:49-59.
  37. [37] Çavuşoğlu Ü, Kaçar S, Pehlivan I, Zengin A. Secure image encryption algorithm design using a novel chaos based S-Box. Chaos, Solitons & Fractals 2017;95:92-101.
  38. [38] Wang Y, Wong K-W, Liao X, Chen G. A new chaos-based fast image encryption algorithm. Appl Soft Comput 2011;11:514-522.
  39. [39] Özkaynak F. Cryptographically secure random number generator with chaotic additional input. Nonlinear Dyn 2014;78:2015-2020.
  40. [40] Hu H, Liu L, Ding N. Pseudorandom sequence generator based on the Chen chaotic system. Comput Phys Commun 2013;184:765-768.
  41. [41] Tang G, Liao X, Chen Y. A novel method for designing S-boxes based on chaotic maps. Chaos, Solitons & Fractals 2005;23:413-419.
  42. [42] Zaibi G, Peyrard F, Kachouri A, Fournier‐Prunaret D, Samet M. Efficient and secure chaotic S-Box for wireless sensor network. Secur Commun Networks 2014;7:279-292.
  43. [43] Liu H, Kadir A, Niu Y. Chaos-based color image block encryption scheme using S-box. AEU-International J Electron Commun 2014;68:676-686.
  44. [44] Özkaynak F, Çelik V, Özer AB. A new S-box construction method based on the fractional-order chaotic Chen system. Signal, Image Video Process 2017;11:659-664.
  45. [45] Precup R-E, Rădac M-B, Tomescu ML, Petriu EM, Preitl S. Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems. Expert Syst Appl 2013;40:188-199.
  46. [46] Zeghlache S, Benslimane T, Amardjia N, Bouguerra A. Interval Type-2 Fuzzy Sliding Mode Controller Based on Nonlinear Observer for a 3-DOF Helicopter with Uncertainties. Int J Fuzzy Syst 2017;19:1444-1463.
  47. [47] Asgharnia A, Shahnazi R, Jamali A. Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms. ISA Trans 2018.
  48. [48] Hsiao F-H. Robust H∞ fuzzy control of dithered chaotic systems. Neurocomputing 2013; 99: 509-20.
  49. [49] Shahnazi R, Haghani A, Jeinsch T. Adaptive fuzzy observer-based stabilization of a class of uncertain time-delayed chaotic systems with actuator nonlinearities. Chaos, Solitons & Fractals 2015;76:98-110.
  50. [50] Shaw R. Strange attractors, chaotic behavior, and information flow. Zeitschrift Für Naturforsch A 1981;36:80-112.
  51. [51] Rukhin A, Soto J, Nechvatal J, Smid M, Barker E. A statistical test suite for random and pseudorandom number generators for cryptographic applications. Booz-Allen and Hamilton Inc Mclean Va; 2001.
  52. [52] Jakimoski G, Kocarev L. Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans Circuits Syst I Fundam Theory Appl 2001;48:163-169.
  53. [53] Ozkaynak F, Yavuz S. Designing chaotic S-Boxes based on time-delay chaotic system. Nonlinear Dyn. 2013; 74:551-557.
  54. [54] Tang G.P., Liao X.F. A method for designing dynamical S-Boxes based on discretized chaotic map. Chaos. Soliton. Frac. 2015; 23:1901-1909.
  55. [55] Chen G. A novel heuristic method for obtaining S-Boxes. Chaos. Soliton. Frac. 2008; 36:1028-1036.
  56. [56] Wang Y., Wong K.W., Liao X.F., Xiang T. A block cipher with dynamic S-Boxes based on tent map. Commun. Nonlinear. Sci. Numer. Simulat. 2009; 14:3089-3099.
  57. [57] Webster AF, Tavares SE. On the design of S-boxes. Conf. theory Appl. Cryptogr. Tech., Springer; 1985, p. 523-34.
  58. [58] Hussain I, Shah T, Mahmood H, Gondal MA. Construction of S8 Liu J S-boxes and their applications. Comput Math with Appl 2012;64:2450-2248.
  59. [59] Biham E, Shamir A. Differential cryptanalysis of DES-like cryptosystems. J Cryptol 1991;4:3-72.
  60. [60] Jantzen J. Design of fuzzy controllers. Tech Univ Denmark, Dep Autom Bldg 1998;326:362-367.
  61. [61] Jones A, Kaufmann A, Zimmermann H-J. Fuzzy sets theory and applications. vol. 177. Springer Science & Business Media; 2012.
  62. [62] C.S. Shieh, FPGA chip with fuzzy PWM control for synchronizing a chaotic system, Control and Intelligent Systems, 40, 2012, 144-150.
  63. [63] A. Ruzitalab, M. H. Farahi, and G. H. Erjaee, Synchronization of multiple chaotic systems using a nonlinear grouping feedback function method, Control and Intelligent Systems, 46, 2018, 1-6.

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