Zhouchao Wei, Yingying Li, and Karthikeyan Rajagopal


  1. [1] 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 attractors in Chua circuits, International Journal of Bifurcation and Chaos, 23, 2013, 1330002.
  2. [2] G.A. Leonov, N.V. Kuznetsov, and T.N. Mokaev, Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion, European Physical Journal Special Topics, 224, 2015, 1421–1458.
  3. [3] G.A. Leonov, N.V. Kuznetsov, and T.N. Mokaev, Homoclinic orbit and hidden attractor in the Lorenz-like system describing the fluid convection motion in the rotating cavity, Communications 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 bifurcation for Kingni-Jafari system with hidden attractors, International Journal of Bifurcation and Chaos, 26, 2016, 1650125.
  5. [5] 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.
  6. [6] T. Kapitaniak and G.A. Leonov, Multistability: Uncovering hidden attractors, European Physical Journal Special Topics, 224, 2015, 1405–1408.
  7. [7] Z. Wang, A. Akgul, V.T. Pham, and S. Jafari, Chaos-based application of a novel no-equilibrium chaotic system with coexisting attractors, Nonlinear Dynamics, 89, 2017, 1877– 1887.
  8. [8] E. Tlelo-Cuautle, L.G. de la Fraga, V.T. Pham, V. Volos, and S. Jafari, Dynamics, FPGA realization and application of a chaotic 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 nested attractors 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 chaotic sea 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 in symmetric chaotic systems, European Physical Journal Special Topics, 224, 2015, 1493–1506.
  12. [12] C.B. Li, J.C. Sprott, and Y. Mei, An infinite 2D lattice of strange attractors, Nonlinear Dynamics, 89, 2017, 2629–2639.
  13. [13] B.C. Bao, H. Bao, N. Wang, M. Chen, and Q. Xu, Hidden extreme multistability in memristive hyperchaotic system, Chaos Solitons and Fractals, 94, 2017, 102–111.
  14. [14] C.B. Li and J.C. Sprott, An infinite 3D quasiperiodic lattice of chaotic attractors, Physics Letters A, 382, 2018, 581–587.
  15. [15] Z.C. Wei, Dynamical behaviors of a chaotic system with no equilibria, Physics Letters A, 376, 2011, 102–108.
  16. [16] 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.
  17. [17] 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.
  18. [18] 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.
  19. [19] 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.
  20. [20] 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.
  21. [21] 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.
  22. [22] 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.
  23. [23] 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.
  24. [24] D. Baleanu, K. Diethelm, E. Scalas, and J.J. Trujillo, Fractional calculus: Models and numerical methods, World Scientific, Singapore, 2014.
  25. [25] Y. Zhou, Basic theory of fractional differential equations, World Scientific, 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 dynamical systems, Physics Reports, 637, 2016, 1–50.
  28. [28] K. Rajagopal, A. Karthikeyan, and A. Srinivasan, FPGA implementation of novel fractional order chaotic system with two equilibriums and no equilibrium and its adaptive sliding mode 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 system applied 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 MHz by 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 of multi-scroll chaotic oscillators, Communications in Nonlinear Science and Numerical Simulation, 27, 2015, 66–80.
  32. [32] Q.X. Wang, S.M. Yu, C.Q. Li, and J.H. Lu, Theoretical design and FPGA-based implementation of high-dimensional digital domain 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, and G. Adam, Fractional order memristor no equilibrium chaotic system with its adaptive sliding mode synchronization and genetically optimized fractional order PID synchronization, Complexity, 2017, 2017, 1892618
  34. [34] H.K. Moffatt, A self-consistent treatment of simple dynamo systems, Geophysical & Astrophysical Fluid Dynamics, 14, 1979, 147–166.
  35. [35] J.H. Bao and D.D. Chen, Coexisting hidden attractors in a 4D segmented disc dynamo with one stable equilibrium or a line equilibrium, Chinese Physics B, 26, 2017, 080201.
  36. [36] E.Z. Dong, Z.H. Liang, and S.Z. Du, Topological horseshoe analysis on a four-wing chaotic attractor and its FPGA implement, 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-based chaotic system and its field programmable gate array implementation, Acta Physica Sinica, 65(12), 2016, 120503.
  39. [39] K. Rajagopal, L. Guessas, S. Vaidyanathan, A. Karthikeyan, and A. Srinivasan, Dynamical analysis and FIGA implementation of a novel hyperchaotic system and its synchronization using adaptive sliding mode control and genetically optimized PID control, Mathematical Problems in Engineering, 2017, 2017, 7307452.
  40. [40] C.S. Shieh, FPGA chip with fuzzy PWM control for synchronizing a chaotic system, Control and Intelligent Systems, 40, 2012, 144–150.
  41. [41] 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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