Zhouchao Wei,∗ Yingying Li,∗ and Karthikeyan Rajagopal∗∗


  1. [1] G.A. Leonov and N.V. Kuznetsov, Hidden attractors in dynam-ical systems. From hidden oscillations in Hilbert-Kolmogorov,Aizerman, and Kalman problems to hidden chaotic attractorsin Chua circuits, International Journal of Bifurcation andChaos, 23, 2013, 1330002.
  2. [2] G.A. Leonov, N.V. Kuznetsov, and T.N. Mokaev, Homoclinicorbits, and self-excited and hidden attractors in a Lorenz-likesystem describing convective fluid motion, European PhysicalJournal Special Topics, 224, 2015, 1421–1458.
  3. [3] G.A. Leonov, N.V. Kuznetsov, and T.N. Mokaev, Homoclinicorbit and hidden attractor in the Lorenz-like system describingthe fluid convection motion in the rotating cavity, Communi-cations in Nonlinear Science and Numerical Simulation, 28,2015, 166–174.
  4. [4] Z.C. Wei, I. Moroz, Z. Wang, J.C. Sprott, and T. Kapitaniak,Dynamics at infinity, degenerate Hopf and zero-Hopf bifurca-tion for Kingni-Jafari system with hidden attractors, Interna-tional Journal of Bifurcation and Chaos, 26, 2016, 1650125.
  5. [5] 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.
  6. [6] T. Kapitaniak and G.A. Leonov, Multistability: Uncoveringhidden attractors, European Physical Journal Special Topics,224, 2015, 1405–1408.
  7. [7] Z. Wang, A. Akgul, V.T. Pham, and S. Jafari, Chaos-basedapplication of a novel no-equilibrium chaotic system withcoexisting attractors, Nonlinear Dynamics, 89, 2017, 1877–1887.
  8. [8] E. Tlelo-Cuautle, L.G. de la Fraga, V.T. Pham, V. Volos, andS. Jafari, Dynamics, FPGA realization and application of achaotic system with an infinite number of equilibrium points,Nonlinear Dynamics, 89, 2017, 1129–1139.
  9. [9] J.C. Sprott, S. Jafari, A.J.M. Khalaf, and T. Kapitaniak,Megastability: Coexistence of a countable infinity of nestedattractors in a periodically-forced oscillator with spatially-periodic damping, European Physical Journal Special Topics,226, 2017, 1979–1985.
  10. [10] S. Jafari, V.T. Pham, and T. Kapitaniak, Multiscroll chaoticsea obtained from a simple 3D system without equilibrium,International Journal of Bifurcation and Chaos, 26, 2016,1650031.
  11. [11] C.B. Li, W. Hu, J.C. Sprott, and X. Wang, Multistability insymmetric chaotic systems, European Physical Journal SpecialTopics, 224, 2015, 1493–1506.
  12. [12] C.B. Li, J.C. Sprott, and Y. Mei, An infinite 2D lattice ofstrange attractors, Nonlinear Dynamics, 89, 2017, 2629–2639.
  13. [13] B.C. Bao, H. Bao, N. Wang, M. Chen, and Q. Xu, Hidden ex-treme multistability in memristive hyperchaotic system, ChaosSolitons and Fractals, 94, 2017, 102–111.
  14. [14] C.B. Li and J.C. Sprott, An infinite 3D quasiperiodic latticeof chaotic attractors, Physics Letters A, 382, 2018, 581–587.
  15. [15] Z.C. Wei, Dynamical behaviors of a chaotic system with noequilibria, Physics Letters A, 376, 2011, 102–108.
  16. [16] 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.
  17. [17] V.-T. Pham, C. Volos, S. Jafari, Z.C. Wei, and X. Wang, Con-structing a novel no-equilibrium chaotic system, InternationalJournal of Bifurcation and Chaos, 24, 2014, 1450073.
  18. [18] 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.
  19. [19] Z.C. Wei and I. Pehlivan, Chaos, coexisting attractors, andcircuit design of the generalized Sprott C system with onlytwo stable equilibria, Optoelectronics and Advanced Materials-Rapid Communications, 6, 2012, 742–745.
  20. [20] V.-T. Pham, S. Jafari, C. Volos, S. Vaidyanathan, and T.Kapitaniak, A chaotic system with infinite equilibria locatedon a piecewise linear curve, Optik-International Journal forLight and Electron Optics, 127, 2016, 9111–9117.
  21. [21] S. Jafari, J.C. Sprott, and M. Molaie, A simple chaotic flowwith a plane of equilibria, International Journal of Bifurcationand Chaos, 26, 2016, 1650098.
  22. [22] 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.
  23. [23] 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.
  24. [24] D. Baleanu, K. Diethelm, E. Scalas, and J.J. Trujillo, Fractionalcalculus: Models and numerical methods, World Scientific,Singapore, 2014.
  25. [25] Y. Zhou, Basic theory of fractional differential equations, WorldScientific, Singapore, 2014.
  26. [26] K. Diethelm, The analysis of fractional differential equations(Berlin: Springer, 2010).63
  27. [27] 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.
  28. [28] K. Rajagopal, A. Karthikeyan, and A. Srinivasan, FPGAimplementation of novel fractional order chaotic system withtwo equilibriums and no equilibrium and its adaptive slidingmode synchronization, Nonlinear Dynamics, 87, 2017, 2281–2304.
  29. [29] E. Tlelo-Cuautle, V.H. Carbajal-Gomez, and P.J. Obeso-Rodelo, FPGA realization of a chaotic communication systemapplied to image processing, Nonlinear Dynamics, 82, 2015,1879–1892.
  30. [30] E. Tlelo-Cuautle, A.D. Pano-Azucena, and J.J. Rangel-Magdaleno, Generating a 50-scroll chaotic attractor at 66 MHzby using FPGAs, Nonlinear Dynamics, 85, 2016, 2143–2157.
  31. [31] E. Tlelo-Cuautle, J.J. Rangel-Magdaleno, A.D. Pano-Azucena,P.J. Obeso-Rodelo, and J.C. Nunez-Perez, FPGA realization ofmulti-scroll chaotic oscillators, Communications in NonlinearScience and Numerical Simulation, 27, 2015, 66–80.
  32. [32] Q.X. Wang, S.M. Yu, C.Q. Li, and J.H. L¨u, Theoretical designand FPGA-based implementation of high-dimensional digitaldomain chaotic systems with random bits iterative update,IEEE Transactions on Circuits and Systems I: Regular Papers,63, 2016, 401–412.
  33. [33] K. Rajagopal, G. Laarem, A. Karthikeyan, A. Srinivasan, andG. Adam, Fractional order memristor no equilibrium chaoticsystem with its adaptive sliding mode synchronization andgenetically optimized fractional order PID synchronization,Complexity, 2017, 2017, 1892618
  34. [34] H.K. Moffatt, A self-consistent treatment of simple dynamosystems, Geophysical & Astrophysical Fluid Dynamics, 14,1979, 147–166.
  35. [35] J.H. Bao and D.D. Chen, Coexisting hidden attractors in a4D segmented disc dynamo with one stable equilibrium or aline equilibrium, Chinese Physics B, 26, 2017, 080201.
  36. [36] E.Z. Dong, Z.H. Liang, and S.Z. Du, Topological horseshoeanalysis on a four-wing chaotic attractor and its FPGA imple-ment, Nonlinear Dynamic, 83, 2016, 623–630.
  37. [37] V. Rashtchi and M. Nourazar, FPGA implementation of a real-time weak signal detector using a duffing oscillator, Circuits,Systems, and Signal Processing, 34, 2015, 3101–3119.
  38. [38] Y.M. Xu, L.D. Wang, and S.K. Duan, A memristor-basedchaotic system and its field programmable gate array imple-mentation, Acta Physica Sinica, 65(12), 2016, 120503.
  39. [39] K. Rajagopal, L. Guessas, S. Vaidyanathan, A. Karthikeyan,and A. Srinivasan, Dynamical analysis and FIGA implemen-tation of a novel hyperchaotic system and its synchronizationusing adaptive sliding mode control and genetically optimizedPID control, Mathematical Problems in Engineering, 2017,2017, 7307452.
  40. [40] C.S. Shieh, FPGA chip with fuzzy PWM control for synchro-nizing a chaotic system, Control and Intelligent Systems, 40,2012, 144–150.
  41. [41] 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.

Important Links:

Go Back