179
Views
29
CrossRef citations to date
0
Altmetric
Articles

NAC-based Synchronisation and Anti-synchronisation Between Hyperchaotic and Chaotic Systems, Its Analogue Circuit Design and Application

, &

REFERENCES

  • T. M. Lakshmanan and K. Murali, Chaos in Nonlinear Oscillators: Controlling and Synchronisation. Singapore: World Scientific, 1996.
  • B. Blasius, A. Huppert, L. Stone. (1999). “Complex dynamics and phase synchronisation in spatially extended ecological system,” Nature. 399, pp. 354–359.
  • N. Hemati. (1994). “Strange attractors in brushless DC motor,” IEEE Trans. Circuits Syst.. 41, pp. 40–45.
  • D. Q. Wei, L. Wan, X. S. Luo, S. Y. Zeng and B. Zhang. (2014). “Global exponential stabilization for chaotic brushless DC motors with a single input,” Nonlinear Dyn. 77, pp. 209–212.
  • L. Antonio. (2009). “Robust linear control of (chaotic) permanent-magnet synchronous motor with uncertainties,” IEEE Trans. Circuits Syst.. 56, pp. 2109–2122.
  • M. P. Aghababa and H. P. Aghababa. (2012). “Synchronisation of nonlinear chaotic electromechanical gyrostat systems with uncertainties,” Nonlinear Dyn. 67, pp. 2689–270.
  • X. Wu and B. Chen. (2013). “Bifurcations and stability of a discrete singular bioeconomic system,” Nonlinear Dyn. 73, pp. 1813–1828.
  • O. A. Gonzales, G. Han, J. P. de Gyvez and E. Sanchez-Sinencio. (2008). “Lorenz based chaotic cryptosystem: A monolithic implementation,” IEEE Trans. Circuits Syst. . 47, pp. 1243–1247.
  • S. J. Sathya Theesar and P. Balasubramaniam. (2014). “Secure communication via synchronisation of Lur'e systems using sampled-data controller,” Circuits. Syst. Signal Process. 33, pp. 37–52.
  • Z. Li and G. Chen. (2006). “Global synchronisation and asymptotic stability of complex dynamical networks,” IEEE Trans. Circuits Syst.. 53, pp. 28–33.
  • G. M. Mahmoud, M. E. Ahmed and N. Sabor. (2011). “On autonomous and nonautonomous modified hyperchaotic complex Lu systems,” Int. J. Bifur. Chaos. 21 (7), pp. 1913–1926.
  • G. M. Mahmoud, E. E. Mahmoud and A. A. Arafa. (2013). “On projective synchronisation of hyperchaotic complex nonlinear systems based on passive theory for secure communications,” Phys. Scripta. 87 (5), pp. 055002.
  • G. M. Mahmoud, E. E. Mahmoud and A. A. Arafa. (2013). “Passive control of n-dimensional chaotic complex nonlinear systems,” J. Vib. Control. 19 (7), pp. 1061–1071.
  • G. M. Mahmoud, E. E. Mahmoud and A. A. Arafa. (2017). “Projective synchronisation for coupled partially linear complex‐variable systems with known parameters,” Math. Method. Appl. Sci. 40 (4), pp. 1214–1222.
  • Z. Wei and Wei Zhang. (2014). “Hidden hyperchaotic attractors in a modified Lorenz–Stenflo system with only one stable equilibrium,” Int. J. Bifurcation Chaos. 24 (10), 1450127.
  • Z. Wei, W. Zhang, Z. Wang and M. Yao. (2015). “Hidden attractors and dynamical behaviours in an extended Rikitake system,” Int. J. Bifurcation Chaos. 25 (2), 1550028.
  • Z. Wei, W. Zhang and M. Yao. (2015). “On the periodic orbit bifurcating from one single non-hyperbolic equilibrium in a chaotic jerk system,” Nonlinear Dyn. 82, pp. 1251–1258.
  • Z. Wei, P. Yu, W. Zhang and M. Yao. (2015). “Study of hidden attractors, multiple limit cycles from Hopf bifurcation and boundedness of motion in the generalised hyperchaotic Rabinovich system,” Nonlinear Dyn. 82, pp. 131–141.
  • Z. Wei, I. Moroz, J. C. Sprott, Z. Wang and W. Zhang. (2017). “Detecting hidden chaotic regions and complex dynamics in the self-exciting homopolar disc dynamo,” Int. J. Bifurcation Chaos. 27 (2), 1730008.
  • Z. Wei, I. Moroz, J. C. Sprott, A. Akgul and W. Zhang. (2017). “Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo,” Chaos. 27 (3), 033101.
  • H. Fujisaka and T. Yamada. (1983). “Stability theory of synchronised motion in coupled-oscillator systems,” Prog. Theory Phys. 69, pp. 32–47.
  • L. M. Pecora and T. L. Carroll. (1990). “Synchronisation in chaotic systems,” Phys. Rev. Lett. 64, pp. 821–824.
  • E. Ott, C. Grebogi and J. A. Yorke. (1990). “Controlling chaos," Phys. Rev. Lett. 64, pp. 1196–1199.
  • L. M. Pecora and T. M. Carroll. (1991). “Synchronizing chaotic circuits,” IEEE Trans. Circuits Syst. 38, pp. 453–456.
  • C. F. Feng. (2010). “Projective synchronisation between two different time-delayed chaotic systems using active control approach,” Nonlinear Dyn. 62, pp. 453–459.
  • P. P. Singh, J. P. Singh and B. K. Roy. (2014). “Synchronisation and anti-synchronisation of Lu and Bhalekar-Gejji chaotic systems using nonlinear active control,” Chaos Solitons Fractals. 69, pp. 31–39.
  • L. Pan, W. Zhou, J. Fang and D. Li. (2010). “A novel active pinning control for synchronisation and anti-synchronisation of new uncertain unified chaotic systems,” Nonlinear Dyn. 62, pp. 417–425.
  • H. T. Yau. (2004). “Design of adaptive sliding mode controller for chaos synchronisation with uncertainties,” Chaos Solitons. Fractals. 22, pp. 341–347.
  • P. P. Singh, J. P. Singh and B. K. Roy. (2016). “Implementation for synchronisation of Chen and Liu-Yang chaotic systems using SMC and active control schemes,” Int. J. Control Theory Appl. 9 (39), pp. 159–169.
  • R. Rakkiyappan, R. Sivasamy and X. Li. (2015). “Synchronisation of identical and nonidentical memristor-based chaotic systems via active backstepping control technique,” Circuits Syst. Signal Process. 34, pp. 763–778.
  • C.-C Yang. (2012). “Adaptive synchronisation of Lu hyperchaotic system with uncertain parameters based on single-input controller,” Nonlinear Dyn. 63, pp. 447–454.
  • L. F. Buscarino, M. Frasca and G. Sciuto. (2011) “Design of time-delay chaotic electronic circuits,” IEEE Trans. Circuits. Syst. . 58, pp. 1888–1896.
  • J. Cao, R. Sivasamy and R. Rakkiyappan. (2015). “Sampled-data synchronisation of chaotic Lur'e systems with time delay,” Circuits Syst. Signal Process. 24 (3), pp. 410–421
  • P. P. Singh, J. P. Singh and B. K. Roy, “Nonlinear observer based synchronisation of Lorenz-Stenflo chaotic systems: a linear matrix inequality approach,” in Proceedings of the Indian Control Conference, Chennai, 2015, pp. 108–111.
  • M. G. Rosenblum, Arkady S. Pikovsky and J. Kurths. (1997). “Phase synchronisation in driven and coupled chaotic oscillators,” IEEE Trans. Circuits. Syst.. 44, pp. 874–881.
  • Q. Miao, Y. Tang, S. Lu and J. Fan. (2009). “Lag synchronisation of a class of chaotic systems with unknown parameters. Nonlinear Dyn. 57, pp. 107–112.
  • M. G. Rosenblum, A. S. Pikovsky and J. Kurths. (1997). “From phase to lag synchronisation in coupled chaotic oscillators,” Phys. Rev. Lett. 78, pp. 4193–4196.
  • D. Ghosh and S. Bhattachary. (2010). “Projective synchronisation of new hyperchaotic system with fully unknown parameters,” Nonlinear Dyn. 61, pp. 11–21.
  • Y. Xu, W. Zhou and J. Fang. (2009). “Hybrid dislocated control and general hybrid projective dislocated synchronisation for the modified Lu chaotic system,” Chaos Solitons Fractals. 42, pp. 1305–1315.
  • X. Wu and H. T. Lu. (2011). “Generalised projective lag synchronisation between different hyperchaotic systems with uncertain parameters,” Nonlinear Dyn. 66, pp. 185–200.
  • W. He and J. Cao. (2010). “Exponential synchronisation of hybrid coupled networks with delayed coupling,” IEEE Trans. Neural Net. 21, pp. 571–583.
  • M. M. Al-Sawalha and M. S. M. Noorani. (2009). “On anti-synchronisation of chaotic systems via nonlinear control,” Chaos Solitons Fractal. 42, pp. 170–179.
  • P. P Singh, J. P. Singh and B. K. Roy. (2016). “SMC based synchronisation and anti- synchronisation of chaotic systems for secure communication and analog circuit realisation,” Int. J. Control Theory Ap. 9 (39), pp. 171–183.
  • M. M. Al-Sawalha and M. S. M. Noorani. (2008). “Active anti-synchronisation between identical and distinctive hyperchaotic systems,” Open Syst. Inform. Dyn. 15, pp. 371–382.
  • S. J. S. Theesar, S. Banerjee and P. Balasubramaniam. (2012). “Synchronisation of chaotic systems under sampled-data control,” Nonlinear Dyn. 70, pp. 1977–1987.
  • Wu-Hua Chen, Z. Wang and X. Lu. (2012). “On sampled-data control for master-slave synchronisation of chaotic Lur'e systems,” IEEE Trans. Circuits. Syst. 59, pp. 515–519.
  • D. Chen, R. Zhang, X. Ma and S. Liu. (2012). “Chaotic synchronisation and anti-synchronisation for a novel class of multiple chaotic systems via a sliding mode control scheme,” Nonlinear Dyn. 69, pp. 35–55.
  • S. Singh and B. B. Sharma, “Sliding mode control based anti-synchronisation scheme for hyperchaotic Lu systems,” in Proceedings of the IEEE International Conference on Communication Systems and Network Technologies, Jammu, 2011, pp. 382–386. doi: 10.1109/CSNT.2011.85
  • P. Wang, D. Li and Q. Hu. (2010). “Bounds of the hyperchaotic Lorenz-Stenflo system,” Commun. Nonlinear Sci. Numer. Simul. 15, pp. 2514–2520.
  • Y. Li. (2005). “Generating hyperchaos via state feedback control. Int. J. Bifurcation Chaos. 15, pp. 3367–3375
  • M. Ghommem, A. H. Nayfeh and M. R. Hajj. (2010). “Control of limit cycle oscillations of a two-dimensional aeroelastic system,” Math. Probl. Eng. 2010, pp. 782457.
  • J. -J. E. Slotine and W. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice Hall, 1991.
  • C. H. Yang and Cheng-Lin Wu. (2014). “Nonlinear dynamic analysis and synchronisation of four-dimensional Lorenz-Stenflo system and its circuit experimental implementation,” Abstr. Appl. Anal. 2014, pp. 213694.
  • Y. Li, W. K. S. Tang and G. Chen. (2005). “Generating hyperchaos via state feedback control,” Int. J. Bifurcation Chaos. 15(10), pp. 3367–3375.
  • E. Z. Dong, Z. Q. Chen, Z. P. Chen and J. Y. Ni. (2012). “Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system,” Chin. Phys. B. 21, pp. 030501–9.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.