A NOVEL S-BOX DESIGN ALGORITHM AND FUZZY-PID CONTROLLER DESIGN FOR A 5-D BURKE–SHAW SYSTEM WITH HIDDEN HYPERCHAOS, 106-121.

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

References

  1. [1] J.C. Sprott, Some simple chaotic flows, Physical Review E, 50,1994, 647–650.
  2. [2] L.P. ˇSil’nikov, A contribution to the problem of the structureof an extended neighborhood of a rough equilibrium state ofsaddle-focus type, Mathematics of the USSR-Sbornik, 10, 1970,91–102.
  3. [3] C.P. Silva, Shil’nikov’s theorem-a tutorial, IEEE Transactionson Circuits and Systems I: Fundamental Theory and Applications, 40, 1993, 675–682.
  4. [4] T. Zhou and G. Chen, Classification of chaos in 3-D autonomous quadratic systems-I: Basic framework and methods,International Journal of Bifurcation and Chaos, 16, 2006,2459–2479.
  5. [5] L. Feng and J. Yinlai, Hopf bifurcation analysis and numericalsimulation in a 4D-hyoerchaotic system, Nonlinear Dynamics,67, 2012, 2857–2864.
  6. [6] H.S. Nik and R.A. Van Gorder, Competitive modes for theBaier-Sahle hyperchaotic flow in arbitrary dimensions, Non-linear Dynamics, 74, 2013, 581–590.
  7. [7] Y. Chen and Q. Yang, Dynamics of a hyperchaotic Lorenz-typesystem, Nonlinear Dynamics, 77, 2014, 569–581.
  8. [8] G. Hu, Generating hyperchaotic attractors with three positiveLyapunov exponents via state feedback control, InternationalJournal of Bifurcation and Chaos, 19, 2009, 651–660.
  9. [9] Q. Yang and C. Chen, A 5D hyperchaotic system with threepositive Lyapunov exponents coined, International Journal ofBifurcation and Chaos, 23, 2013, 1350109.
  10. [10] Q. Yang, W.M. Osman, and C. Chen, A new 6D hyperchaoticsystem with four positive Lyapunov exponents coined, Inter-national Journal of Bifurcation and Chaos, 25, 2015, 1550060.
  11. [11] G.A. Leonov and N.V. Kuznetsov, Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov,Aizerman, and Kalman problems to hidden chaotic attractor inChua circuits, International Journal of Bifurcation and Chaos,23, 2013, 1330002.
  12. [12] G.A.Leonov, N.V. Kuznetsov, and T.N. Mokaev, Hidden at-tractor and homoclinic orbit in Lorenz-like system describingconvective fluid motion in rotating cavity, Communicationsin Nonlinear Science and Numerical Simulation, 28, 2015,166–174.
  13. [13] N.V. Kuznetsov and G.A. Leonov, Numerical Visualization ofattractors: Self-exciting and hidden attractors, Handbook ofApplications of Chaos Theory, CRC Press, 2016, 135–143.
  14. [14] G.A. Leonov, N.V. Kuznetsov, V.I. Vagaitsev, Localizationof hidden Chua’s attractors, Physics Letters A, 375, 2011,2230–2233.
  15. [15] G.A. Leonov, N.V. Kuznetsov, and V.I. Vagaitsev, Hiddenattractor in smooth Chua systems, Physica D: NonlinearPhenomena, 241, 2012, 1482–1486.
  16. [16] Z.C. Wei, Dynamical behaviors of a chaotic system with noequilibria, Physics Letters A, 376, 2011, 102–108.
  17. [17] Z.C. Wei, R.R. Wang, and A.P. Liu, A new finding of theexistence 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, InternationalJournal 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, InternationalJournal of Bifurcation and Chaos, 23, 2013, 1350188.
  20. [20] Z.C. Wei, W. Zhang, Z. Wang, and M.H. Yao, Hidden attractorsand 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, andcircuit design of the generalized Sprott C system with only twostable equilibria, Optoelectronics and Advanced Materials-rapidCommunications, 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 a5D self-exciting homopolar disc dynamo, Chaos, 27(3), 2017,033101.
  23. [23] V.-T. Pham, S. Jafari, C. Volos, S. Vaidyanathan, andT. Kapitaniak, A chaotic system with infinite equilibria locatedon a piecewise linear curve, Optik-International Journal forLight and Electron Optics, 127, 2016, 9111–9117.
  24. [24] S. Jafari, J.C. Sprott, and M. Molaie, A simple chaotic flowwith a plane of equilibria, International Journal of Bifurcationand 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, NonlinearDynamics, 86, 2016, 1349–1358.
  26. [26] C. Li, A. Akgul, J.C. Sprott, H.C. Iu, and W. Thio, A symmetricpair of hyperchaotic attractors, International Journal of CircuitTheory & Applications, 46, 2018, 2434–2443.
  27. [27] C. Li, J.C. Sprott, T. Kapitaniak, and T. Lu, Infinite latticeof hyperchaotic strange attractors, Chaos, Solitons & Fractals,109, 2018, 76–82.
  28. [28] Z. Wang, S. Cang, E.O. Ochola, and Y. Sun, A hyperchaoticsystem without equilibrium, Nonlinear Dynamics, 69, 2012,531–537.
  29. [29] Z. Wei, R. Wang, A. Liu, A new finding of the existence ofhidden hyperchaotic attractors with no equilibria, Mathematicsand Computers in Simulation, 100, 2014, 13–23.
  30. [30] G.M. Mahmoud, E.E. Mahmoud, and M.E. Ahmed, On thehyperchaotic complex L¨u system, Nonlinear Dynamics, 58,2009, 725–738.
  31. [31] Z. Wei, P. Yu, W. Zhang, and M. Yao, Study of hidden attractors, multiple limit cycles from Hopf bifurcation and boundedness of motion in the generalized hyperchaotic Rabinovichsystem, Nonlinear Dynamics, 82, 2015, 131–141.
  32. [32] Z. Wei and W. Zhang, Hidden hyperchaotic attractors in amodified Lorenz-Stenflo system with only one stable equilibrium, International Journal of Bifurcation and Chaos, 24,2014, 1450127.
  33. [33] D. Dudkowski, S. Jafari, T. Kapitaniak, N.V. Kuznetsov,G.A. Leonov, and A. Prasad, Hidden attractors in dynamicalsystems, Physics Reports, 637, 2016, 1–50.
  34. [34] T. Kapitaniak and G.A. Leonov, Multistability: Uncoveringhidden attractors, European Physical Journal Special Topics,224(8), 2015, 1405–1408.
  35. [35] I. Pehlivan and Y. Uyaro˘glu, A new 3D chaotic system withgolden proportion equilibria: Analysis and electronic circuitrealization, Computers & Electrical Engineering, 38, 2012,1777–1784.
  36. [36] I. Koyuncu, A.T. Ozcerit, and I. Pehlivan, Implementationof FPGA-based real time novel chaotic oscillator, NonlinearDynamics, 77, 2014, 49–59.
  37. [37] ¨U. C¸avu¸so˘glu, S. Ka¸car, I. Pehlivan, and A. Zengin, Secureimage encryption algorithm design using a novel chaos basedS-Box, Chaos, Solitons & Fractals, 95, 2017, 92–101.
  38. [38] Y. Wang, K.-W. Wong, X. Liao, and G. Chen, A new chaos-based fast image encryption algorithm, Applied Soft Computing, 11, 2011, 514–522.
  39. [39] F. ¨Ozkaynak, Cryptographically secure random number generator with chaotic additional input, Nonlinear Dynamics, 78,2014, 2015–2020.
  40. [40] H. Hu, L. Liu, and N. Ding, Pseudorandom sequence generator based on the Chen chaotic system, Computer PhysicsCommunications, 184, 2013, 765–768.
  41. [41] G. Tang, X. Liao, and Y. Chen, A novel method for designingS-boxes based on chaotic maps, Chaos, Solitons & Fractals,23, 2005, 413–419.
  42. [42] G. Zaibi, F. Peyrard, A. Kachouri, D. Fournier-Prunaret, andM. Samet, Efficient and secure chaotic S-Box for wirelesssensor network, Security and Communication Networks, 7,2014, 279–292.
  43. [43] H. Liu, A. Kadir, and Y. Niu, Chaos-based color image blockencryption scheme using S-box, AEU – International Journalof Electronics and Communications, 68, 2014, 676–686.
  44. [44] F. ¨Ozkaynak, V. C¸elik, and A.B. ¨Ozer, A new S-box construction method based on the fractional-order chaotic Chensystem, Signal, Image Video Process, 11, 2017, 659–664.
  45. [45] R.-E. Precup, M.-B. Rdac, M.L. Tomescu , E.M. Petriu, and S.Preitl, Stable and convergent iterative feedback tuning of fuzzycontrollers for discrete-time SISO systems, Expert Systems withApplications, 40, 2013, 188–199.
  46. [46] S. Zeghlache, T. Benslimane, N. Amardjia, and A. Bouguerra,Interval type-2 fuzzy sliding mode controller based on non-linear observer for a 3-DOF helicopter with uncertainties,International Journal of Fuzzy Systems, 19, 2017, 1444–1463.
  47. [47] A. Asgharnia, R. Shahnazi, and A. Jamali, Performance androbustness of optimal fractional fuzzy PID controllers for pitchcontrol of a wind turbine using chaotic optimization algorithms,ISA Transactions, 79, 2018, 27–44.
  48. [48] F.-H. Hsiao, Robust H∞ fuzzy control of dithered chaoticsystems, Neurocomputing, 99, 2013, 509–520.
  49. [49] R. Shahnazi, A. Haghani, and T. Jeinsch, Adaptive fuzzyobserver-based stabilization of a class of uncertain time-delayedchaotic systems with actuator nonlinearities, Chaos, Solitons& Fractals, 76, 2015, 98–110.
  50. [50] R. Shaw, Strange attractors, chaotic behavior, and informationflow, Zeitschrift f¨ur Naturforsch A, 36, 1981, 80–112.
  51. [51] A. Rukhin, J. Soto, J. Nechvatal, M. Smid, and E. Barker,A statistical test suite for random and pseudorandom numbergenerators for cryptographic applications (McLean, VA: Booz-Allen and Hamilton Inc., 2001).
  52. [52] G. Jakimoski and L. Kocarev, Chaos and cryptography: Blockencryption ciphers based on chaotic maps, IEEE Transactions on Circuits and Systems I: Fundamental Theory andApplications, 48, 2001, 163–169.
  53. [53] F. Ozkaynak, and S. Yavuz, Designing chaotic S-Boxes basedon time-delay chaotic system, Nonlinear Dynamics, 74, 2013,551–557.
  54. [54] G.P. Tang and X.F. Liao, A method for designing dynamicalS-Boxes based on discretized chaotic map, Chaos, Solitons &Fractal, 23, 2015, 1901–1909.
  55. [55] G. Chen, A novel heuristic method for obtaining S-Boxes,Chaos, Solitons & Fractal, 36, 2008, 1028–1036.
  56. [56] Y. Wang, K.W. Wong, X.F. Liao, T. Xiang, A block cipherwith dynamic S-Boxes based on tent map, Communicationsin Nonlinear Science and Numerical Simulation, 14, 2009,3089–3099.
  57. [57] A.F. Webster and S.E. Tavares, On the design of S-boxes,Lecture Notes in Computer Science, 218, 1986, 523–534.
  58. [58] I. Hussain, T. Shah, H. Mahmood, and M.A. Gondal, Con-struction of S8 Liu J S-boxes and their applications, Computers& Mathematics with Applications, 64, 2012, 2450–2248.
  59. [59] E. Biham and A. Shamir, Differential cryptanalysis of DES-likecryptosystems, Journal of Cryptology, 4, 1991, 3–72.
  60. [60] J. Jantzen, Design of fuzzy controllers, Technical Universityof Denmark, Dep Autom Bldg, 326, 1998, 362–367.
  61. [61] A. Jones, A. Kaufmann, and H.-J. Zimmermann, Fuzzy setstheory and applications, vol. 177 (Springer Science & BusinessMedia, 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, Synchronizationof multiple chaotic systems using a nonlinear grouping feedbackfunction method, Control and Intelligent Systems, 46, 2018,1–6.

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