Design and implementation of grid multiwing hyperchaotic lorenz system family via switching control and constructing super-heteroclinic loops

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 59, Issue 5, 2012, Pages 1015-1028

  Yu, Simin ^a   Lu, Jinhu ^b,c   Yu, Xinghuo ^b   Chen, Guanrong ^d  

^a GUANGDONG UNIVERSITY OF TECHNOLOGY   (China)

^b RMIT UNIVERSITY   (Australia)

^c CHINESE ACADEMY OF SCIENCES   (China)

^d CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Circuit implementation; grid multiwing hyperchaotic attractor; piecewise linear hyperchaotic Lorenz system family; super heteroclinic loop; switching control

Indexed keywords

DYNAMICAL SYSTEMS; INTEGRATED CIRCUIT MANUFACTURE; LINEAR SYSTEMS; STATE FEEDBACK; SWITCHING;

CIRCUIT IMPLEMENTATION; GRID MULTIWING HYPERCHAOTIC ATTRACTORS; PIECEWISE LINEAR HYPERCHAOTIC LORENZ SYSTEM FAMILIES; SUPER-HETEROCLINIC LOOP; SWITCHING CONTROL;

PIECEWISE LINEAR TECHNIQUES;

EID: 84860890292     PISSN: 15498328     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2011.2180429     Document Type: Article

References (28)

1. T. Matsumoto, "Chaos in electronic circuits," Proc. IEEE, vol. 75, no. 8, pp. 1033-1057, Aug. 1987.
2. M. A. Aziz-Alaoui, "Differential equations withmultispiral attractors," Int. J. Bifurcation Chaos, vol. 9, no. 6, pp. 1009-1039, Jun. 1999.
3. J. Lü,X.Yu, andG.Chen, "Generating chaotic attractors with multiple merged basins of attraction: A switching piecewise-linear control approach," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 2, pp. 198-207, Feb. 2003.
4. M. E. Yalcin, J. A. K. Suykens, J. Vandewalle, and S. Ozoguz, "Families of scroll grid attractors," Int. J. Bifurcation Chaos, vol. 12, no. 1, pp. 23-41, Jan. 2002. (Pubitemid 34862059)
5. J. Lü, F. Han, X. Yu, and G. Chen, "Generating 3-D multi-scroll chaotic attractors: A hysteresis series switching method," Automatica, vol. 40, no. 10, pp. 1677-1687, Nov. 2004.
6. P. Arena, S. Baglio, L. Fortuna, and G. Manganaro, "Generation of -double scrolls via cellular neural networks," Int. J. Circuit Theory Appl., vol. 24, no. 3, pp. 241-252, May/Jun. 1996. (Pubitemid 126604257)
7. A. Mees and P. Chapman, "Homoclinic and Heteroclinic orbits in the double scroll attractor," IEEE Trans. Circuits Syst., vol. 34, no. 9, pp. 1115-1120, Sep. 1987.
8. T. Matsumoto, L. O. Chua, and K. Kobayashi, "Hyperchaos: Laboratory experiment and numerical confirmation," IEEE Trans. Circuits Syst., vol. 33, no. 11, pp. 1143-1147, Nov. 1986. (Pubitemid 17484189)
9. S. Özoguz, A. S. Elwakil, and M. P. Kennedy, "Experimental verification of the butterfly attractor in a modified Lorenz system," Int. J. Bifurcation Chaos, vol. 12, no. 7, pp. 1627-1632, Jul. 2002.
10. A. S. Elwakil, S. Ozoguz, and M. P. Kennedy, "A four-wing butterfly attractor from a fully autonomous system," Int. J. Bifurcation Chaos, vol. 13, no. 10, pp. 3093-3098, Oct. 2003. (Pubitemid 38034509)
11. M. E. Yalcin, J. A. K. Suykens, and J. Vandewalle, Cellular Neural Networks, Multi-Scroll Chaos and Synchronization. Singapore: World Scientific, 2005.
12. J. A. K. Suykens and J. Vandewalle, "Generation of -double scrolls ," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 11, pp. 861-867, Nov. 1993.
13. R. Miranda and E. Stone, "The proto-Lorenz system," Phys. Lett. A, vol. 178, no. 1-2, pp. 105-113, Jul. 1993.
14. J. Lü, S. M. Yu, H. Leung, and G. Chen, "Experimental verification of multi-directional multi-scroll chaotic attractors," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 1, pp. 149-165, Jan. 2006. (Pubitemid 43141938)
15. J. Lü and G. Chen, "Generating multi-scroll chaotic attractors: Theories, methods and applications," Int. J. Bifurcation Chaos, vol. 16, no. 4, pp. 775-858, Apr. 2006. (Pubitemid 43936686)
16. C. P. Silva, "Shil'nikov's theorem-A tutorial," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 10, pp. 675-682, Oct. 1993.
17. L. O. Chua, M. Komuro, and T. Matsumoto, "The double scroll family," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. CSI-33, no. 11, pp. 1072-1118, Nov. 1986.
18. L. P. Shil'nikov, "Chua's circuit: Rigorous results and future problems," IEEE Trans. Circuits Syst. I, vol. CSI-40, no. 10, pp. 784-786, Oct. 1993.
19. A. I. Mees and P. B. Chapman, "Homoclinic and heteroclinic orbits in the double scroll attractor," IEEE Trans. Circuits Syst. I, vol. 34, no. 9, pp. 1115-1120, Sep. 1987.
20. Z. Li, G. Chen, andW. A. Halang, "Homoclinic and heteroclinic orbits in a modified Lorenz system," Inf. Sci., vol. 165, no. 3, pp. 235-245, Oct. 2004.
21. G. Li and X. Chen, "Constructing piecewise linear chaotic system based on the heteroclinic Shil'nikov theorem," Communicat. Non. Sci. Numer. Simulat., vol. 14, no. 1, pp. 194-203, Jan. 2009.
22. S. Yu, J. Lü, G. Chen, and X. Yu, "Generating grid multiwing chaotic attractors by constructing heteroclinic loops into switching systems," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 58, no. 5, pp. 314-318, May 2011.
23. J. Lü, G. Chen, X. Yu, and H. Leung, "Design and analysis of multiscroll chaotic attractors from saturated function series," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 12, pp. 2476-2490,Dec. 2004. (Pubitemid 40009469)
24. E. N. Lorenz, "Deterministic nonperiodic flow," J. Atmos. Sci., vol. 51, no. 3, pp. 130-141, 1963.
25. A. Vanecek and S. Celikovský, Control Systems: From Linear Analysis to Synthesis of Chaos. Englewood Cliffs, NJ: Prentice-Hall, 1996.
26. G. Chen and T. Ueta, "Yet another chaotic attractor," Int. J. Bifurcation Chaos, vol. 9, no. 7, pp. 1465-1466, Jul. 1999. (Pubitemid 129292251)
27. J. Lü and G. Chen, "A new chaotic attractor coined," Int. J. Bifurcation Chaos, vol. 12, no. 3, pp. 659-661, Mar. 2002. (Pubitemid 34862041)
28. S. Yu, J. Lü, G. Chen, and X. Yu, "Design of grid multiwing butterfly chaotic attractors from piecewise Lü system based ond switching control and heteroclinic orbit," in Proc. 2011 IEEE Int. Symp. Circuits Syst. (ISCAS'11), Rio de Janeiro, Brazil, May 15-18, 2011, pp. 1335-1338.