Estimations for ultimate boundary of a new hyperchaotic system and its simulation

Nonlinear Dynamics

Volumn 75, Issue 3, 2014, Pages 529-537

  Zhang, Fuchen ^a   Mu, Chunlai ^a   Wang, Liangwei ^b   Wang, Xingyuan ^c   Yao, Xianzhong ^a  

^a CHONGQING UNIVERSITY   (China)

^b CHONGQING THREE GORGES UNIVERSITY   (China)

^c DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Generalized Lyapunov function; Global exponential attractive set; Hyperchaotic system; Ultimate bound

Indexed keywords

BOUNDEDNESS; EXPONENTIAL RATES; GENERALIZED LYAPUNOV FUNCTIONS; GLOBAL EXPONENTIAL ATTRACTIVE SET; HYPER-CHAOTIC SYSTEMS; HYPERCHAOTIC; NEW HYPERCHAOTIC SYSTEMS; ULTIMATE BOUND;

LYAPUNOV FUNCTIONS;

CHAOTIC SYSTEMS;

EID: 84893836047     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-1082-6     Document Type: Article

References (26)

1. Liao, X.; Fu, Y.; Xie, S.; Yu, P.: Globally exponentially attractive sets of the family of Lorenz systems. Sci. China, Ser. F 51, 283-292 (2008)
2. Chen, G.; Lü, J.: Dynamical Analysis, Control and Synchronization of the Lorenz Systems Family. Science Press, Beijing (2003)
3. Leonov, G.; Bunin, A.; Koksch, N.: Attractor localization of the Lorenz system. Z. Angew. Math. Mech. 67, 649-656 (1987)
4. Leonov, G.: Lyapunov dimension formulas for Henon and Lorenz attractors. St. Petersburg Math. J. 13, 1-12 (2001)
5. Zhang, F.; Shu, Y.; Yang, H.; Li, X.: Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization. Chaos Solitons Fractals 44, 137-144 (2011)
6. Zhang, F.; Shu, Y.; Yang, H.: Bounds for a new chaotic system and its application in chaos synchronization. Commun. Nonlinear Sci. Numer. Simul. 16, 1501-1508 (2011)
7. Jian, J.; Zhao, Z.: New estimations for ultimate boundary and synchronization control for a disk dynamo system. Nonlinear Anal. Hybrid Syst. 9, 56-66 (2013)
8. Zhang, F.; Mu, C.; Li, X.: On the boundedness of some solutions of the Lü system. Int. J. Bifurc. Chaos Appl. Sci. Eng. 22, 1250015 (2012)
9. Zhang, F.; Li, Y.; Mu, C.: Bounds of solutions of a kind of hyper-chaotic systems and application. J. Math. Res. Appl. 33(3), 345-352 (2013)
10. Zhang, J.; Tang, W.: A novel bounded 4D chaotic system. Nonlinear Dyn. 67, 2455-2465 (2012)
11. Pikovski, A.; Rabinovich, M.; Trakhtengerts, V.: Onset of stochasticity in decay confinement of parametric instability. Sov. Phys. JETP 47, 715-719 (1978)
12. Xie, F.; Zhang, X.: Invariant algebraic surfaces of the Rabinovich system. J. Phys. A 36, 499-516 (2003)
13. Llibre, J.; Messias, M.; Silva, P.: On the global dynamics of the Rabinovich system. J. Phys. A 41, 1-21 (2008)
14. Zhang, X.: Integrals of motion of the Rabinovich system. J. Phys. A 33, 5137-5155 (2003)
15. Liu, Y.: Hyperchaotic system from controlled Rabinovich system. IET Control Theory Appl. 28, 1671-1678 (2011)
16. Leonov, G.; Kuznetsov, N.: Time-varying linearization and the Perron effects. Int. J. Bifurc. Chaos Appl. Sci. Eng. 17, 1079-1107 (2007) (Pubitemid 46905045)
17. Leonov, G.; Kuznetsov, N.: Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits. Int. J. Bifurc. Chaos Appl. Sci. Eng. 23, 1330002 (2013)
18. Bragin, V.; Vagaitsev, V.; Kuznetsov, N.; Leonov, G.: Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits. J. Comput. Syst. Sci. Int. 50, 511-543 (2011)
19. Leonov, G.; Kuznetsov, N.; Vagaitsev, V.: Localization of hidden Chua's attractors. Phys. Lett. A 375, 2230-2233 (2011)
20. Boichenko, V.; Leonov, G.; Reitmann, V.: Dimension Theory for Ordinary Differential Equations. Teubner, Wiesbaden (2005)
21. Leonov, G.; Ponomarenko, D.; Smirnova, V.: Frequency Domain Methods for Nonlinear Analysis: Theory and Applications. World Scientific, Singapore (1996)
22. Leonov, G.; Boichenko, V.: Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors. Acta Appl. Math. 26, 1-60 (1992)
23. Chen, G.; Ueta, T.: Yet another chaotic attractor. Int. J. Bifurc. Chaos Appl. Sci. Eng. 9, 1465-1466 (1999) (Pubitemid 129292251)
24. Lü, J.; Chen, G.: A new chaotic attractor coined. Int. J. Bifurc. Chaos Appl. Sci. Eng. 12, 659-661 (2002) (Pubitemid 34862041)
25. Leonov, G.: General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, Lu and Chen systems. Phys. Lett. A 376, 3045-3050 (2012)
26. Lü, J.; Chen, G.: Generating multi-scroll chaotic attractors: theories, methods and applications. Int. J. Bifurc. Chaos Appl. Sci. Eng. 16, 775-858 (2006) (Pubitemid 43936686)