---

Journal of Vibration Testing and System Dynamics 4(4) (2020) 325--336 | DOI:10.5890/JVTSD.2020.12.003

Yuansheng Wang , Bo Li, Guiying Lu

School of Mechanics and Electrical Information, China University of Geoscience Wuhan, Hubei, 430074, China

Download Full Text PDF

 

Abstract

Between two 4-dimensional hyper-chaotic systems with unknown parameters, using Lyapunov stability theory, adaptive controller and parameter estimation law are designed to achieve their globally asymptotical synchronization and anti-synchronization. By numerical calculation with MATLAB, synchronization or anti-synchronization is arrived theoretically but synchronous or anti-synchronous errors of state variables cannot all converge to zero simultaneously during a limited time. The comparative and contrastive studies about system without cubic term indicates that the primary cause is existence of cubic term. It is verified by numerical simulation examples consistently.

Acknowledgments

This research is financially supported by the national major scientific instruments special fund (41827808).

References

1. [1]	Lorenz, E.N. (1963), Deterministic non-periodic flow, Journal of the Atmospheric Science, 20, 130-141.

2. [2]	Chen, G.R. and L\"{u} J.H. (2003), Dynamic Analysis, Control and Synchronization of the Lorenz System Family, Science Press, Beijing, 150-278.

3. [3]	Liu, L., Su, Y.C., and Liu, C.X. (2006), A new chaotic system and its circuit emulation, Acta Physica Sinica, 55(8), 3933-3937.

4. [4]	Wang, G.Y., Qiu, S.S., and Xu, Z.Y. (2006), A new three-dimensional quadratic chaotic system and its circuitry implementation, Acta Physica Sinica, 55(7), 3293-3301.

5. [5]	Li, W.F. and Li, Q.G. (2015), Dynamics analysis, synchronization and anti-synchronization of novel chaotic system, Application Research of Computers, 32(9), 2659-2663.

6. [6]	Zhou, X.Y. (2012), A novel chaotic system and its circuit simulation, Acta Physica Sinica, 61(3), 71-79.

7. [7]	Liu, M.H. and Feng J.C. (2009), A new hyperchaotic system, Acta Physica Sinica, 58(7), 4457-4462.

8. [8]	Wang, G.Y., Qiu S.S., Chen, H., and Cui, J.D. (2008), A new chaotic system and its circuitry design and implementation, Journal of Circuits and Systems, 13(5), 58-60.

9. [9]	Zhang, Y.H., Qi, G.Y., Liu, W.L., and Yan, Y. (2006), Theoretical analysis and circuit implementation of a new four dimensional chaotic system, Acta Physica Sinica, 55(7), 3307-3314.

10. [10]	Luo, M.W., Luo, X.H., and Li, H.Q. (2013), A family of four-dimensional multi-wing chaotic system and its circuit implementation, Acta Physica Sinica, 62(2), 153-158.

11. [11]	Wang, H.Y. and Yin, X. (2017), Dynamical behaviors of a new hyperchaotic system and its adaptive control and synchronization, Journal of Dynamics and Control, 15(4), 335-341.

12. [12]	Huang, S.H. and Tian, L.X. (2011), Dynamical analysis and anti-synchronization for a new four dimensional hyperchaotic system, Journal of Circuits and Systems, 16(6), 66-74.

13. [13]	Long, Z.C. and Ma D.Z. (2016), A new five dimensional hyper-chaotic circuit and its application in secure communication, Open Journal of Circuits and Systems, 5(1), 10-20.

14. [14]	Wang, Z.L. and Niu, H. (2019), Analysis, control and circuit implementation of a novel 4D chaotic system, Dynamical Systems and Control, 8(2), 129-139.

15. [15]	Wei, Q. and Niu, H. (2019), Analysis and circuit design of a novel 5D hyperchaotic system, Dynamical Systems and Control, 8(2), 118-128.

16. [16]	Li, L.P., Wang, B., L\"{u}, X.Y., and Wu, Y. (2017), Chaos-related localization in modulated lattice array, Annalen der physik, 1700218.

17. [17]	Wang, S.B and Wang, X.Y. (2016), Adaptive generalized combination complex synchronization and parameter identification of hyperchaotic complex systems, Journal of Electronics $&$ Information Technology, 38(8), 2062-2067.

18. [18]	Liu, J., Liu, S.T., and Yuan, C.H. (2015), Adaptive complex modified projective synchronization of complex chaotic(hyperchaotic) systems with uncertain complex parameters, Nonlinear Dynamics, 79, 1035-1047.

19. [19]	Sun, J.W., Cui, G.Z., and Wang, Y.F. et al. (2015), Combination complex synchronization of three chaotic complex systems, Nonlinear Dynamics, 79, 953-965.

20. [20]	Luo, C. and Wang, X.Y. (2013), Chaos in the fractional-order complex Lorenz system and its synchronization, Nonlinear Dynamics, 71, 241-257.