Global pulse synchronization of chaotic oscillators through fast-switching: theory and experiments

Chaos, Solitons and Fractals

Volumn 41, Issue 1, 2009, Pages 245-262

  Porfiri, Maurizio ^a   Fiorilli, Francesca ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; CIRCUIT OSCILLATIONS; SYNCHRONIZATION;

CHAOTIC OSCILLATORS; CONSTANT MATRIX; COUPLED CHUA'S CIRCUITS; GLOBAL SYNCHRONIZATION; LYAPUNOV STABILITY THEORY; MASTER-SLAVE CONFIGURATIONS; MATRIX MEASURES; PULSE SYNCHRONIZATION;

SWITCHING THEORY;

EID: 67349233469     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.11.033     Document Type: Article

References (48)

1. Boccaletti S., Kurths J., Osipov G., Valladares D.L., and Zhou C.S. The synchronization of chaotic systems. Phys Reports 366 1 (2002) 1-101
2. In: Chen G., and Yu X. (Eds). Chaos control theory and applications. Lecture notes in control and information sciences vol. 292 (2003), Springer, Berlin
3. Glass L., and Mackey M.C. From clocks to chaos: the rhythms of life (1988), Princeton University Press
4. Gonzalez-Miranda J.M. Synchronization and control of chaos (2004), Imperial College Press, London
5. Pikovsky A., Rosemblum M., and Kurths J. Synchronization, a universal concept in nonlinear sciences (2001), Cambridge University Press, Cambridge
6. Camazine S., Ristine W., and Didion M.E. Self-organization in biological systems (2003), Princeton University Press
7. Buck J., and Buck E. Synchronous fireflies. Scientific American 234 5 (1976) 75-85
8. Kim D. A spiking neuron model for synchronous flashing of fireflies. Bio Systems 76 1-3 (2004) 7-20
9. Collins J.J., and Stewart I. Coupled nonlinear oscillators and the symmetries of animal gaits. J Nonlinear Sci 3 1 (1993) 349-392
10. Guevara M.R., Shirier A., and Glass L. Phase-locked rhythms in periodically stimulated heart cell aggregates. Am J Physiol 254 1 (1988) H1-H10
11. Honerkamp J. The heart as a system of coupled nonlinear oscillators. J Math Biol 19 1 (1983) 69-88
12. Torre V. A theory of synchronization of two heart pacemaker cells. J Theor Biol 61 1 (1976) 55-71
13. Netoff T.I., and Schiff S.J. Decreased neuronal synchronization during experimental seizures. J Neurosci 22 16 (2002) 7297-7307
14. Rapp P., Bashore T.R., Martinerie J.M., Albano A.M., Zimmerman I.D., and Mees A.I. Dynamics of brain electrical activity. Brain Topography 2 1-2 (1989) 99-118
15. Womelsdorf T., and Fries P. The role of neuronal synchronization in selective attention. Current Opin Neurobiol 17 2 (2007) 1-7
16. Cuomo K.M., Oppenheim V.A., and Strogatz S.H. Synchronization of Lorentz-based chaotic circuits with application to communications. IEEE Trans Circuits Systems II 40 10 (1993) 626-633
17. Feki M. An adaptive chaos synchronization scheme applied to secure communication. Chaos, Solitons & Fractals 18 1 (2003) 141-148
18. Feki M., Robert B., Gelle G., and Colas M. Secure digital communication using discrete-time chaos synchronization. Chaos, Solitons & Fractals 18 4 (2003) 881-890
19. Hayes S., Grebogi C., and Ott E. Communicating with chaos. Phys Rev Lett 70 20 (1993) 3031-3034
20. Jovic B., Unsworth C.P., Sandhu G.S., and Berber S.M. A robust sequence synchronization unit for multi-user ds-cdma chaos-based communication systems. Signal Process 87 7 (2007) 1692-1708
21. Miliou A.N., Antoniades I.P., Stavrinides S.G., and Anagnostopulos A.N. Secure communication by chaotic synchronization: Robustness under noisy conditions. Nonlinear Anal Real World Appl 8 3 (2007) 1003-1012
22. Kuramoto Y. Chemical oscillations, waves and turbulence (1984), Springer, Berlin
23. Duane G.S., Webster P.J., and Weiss J.B. Go-occurrence of northern and southern hemisphere blocks as partially synchronized chaos. J Atmos Sci 56 24 (1999) 4183-4205
24. Ohtsubop J. Feedback induced instability and chaos in semiconductor lasers and their applications. Opt Rev 6 1 (1999) 1-15
25. Ge Z., and Chen Y. Synchronization of mutual coupled chaotic systems via partial stability theory. Chaos, Solitons & Fractals 34 3 (2007) 787-794
26. Tsay S., Huang C., Qiu D., and Chen W. Implementation of bidirectional chaotic communication systems based on lorenz circuits. Chaos, Solitons & Fractals 20 3 (2004) 567-579
27. Yu Y., and Zhang S. The synchronization of linearly bidirectional coupled chaotic systems. Chaos, Solitons & Fractals 22 1 (2004) 189-197
28. Carroll T.L., and Pecora L.M. Synchronizing chaotic circuits. IEEE Trans Circuits Systems 38 4 (1991) 453-456
29. Chen H.-H. Global synchronization of chaotic systems via linear balanced feedback control. Chaos, Solitons & Fractals 186 1 (2007) 923-931
30. Fortuna L., Frasca M., and Rizzo A. Experimental pulse synchronization of two chaotic circuits. Chaos, Solitons & Fractals 17 2-3 (2003) 335-361
31. Grassi G., and Mascolo S. Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal. IEEE Trans Circuits Systems I 44 10 (1997) 1011-1014
32. Jiang G.P., Tang W.K.S., and Chen G. A simple global synchronization criterion for coupled chaotic system. Chaos, Solitons & Fractals 15 5 (2003) 925-935
33. Lerescu A.I., Contandache N., Oancea S., and Grosu I. Collection of master-slave synchronized chaotic systems. Chaos, Solitons & Fractals 22 3 (2004) 599-604
34. Park J.H. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons & Fractals 25 3 (2005) 579-584
35. Pecora L.M., and Carroll T.L. Synchronization in chaotic system. Phys Rev Lett 6 8 (1990) 821-824
36. Sun J., and Zhang Y. Some simple global synchronization criterions for coupled time-varying chaotic systems. Chaos, Solitons & Fractals 19 4 (2004) 9398
37. Haeri M., and Khademian B. Comparisons between different synchronization methods of identical chaotic systems. Chaos, Solitons & Fractals 29 4 (2006) 1002-1022
38. Kilic R. Experimental study on impulsive synchronization between two modified chua's circuits. Nonlinear Anal Real World Appl 7 5 (2006) 1298-1303
39. Hale J.K. Ordinary differential equations (1969), John Wiley & Sons, New York
40. Aeyels D., and Peuteman J. On exponential stability of nonlinear time-varying differential equations. Automatica 35 6 (1999) 1091-1100
41. Peuteman J., and Aeyels D. Exponential stability of nonlinear time-varying differential equations and partial averaging. Math Control, Signals System 15 1 (2002) 42-70
42. Ström T. On logarithmic norms. SIAM J Numer Anal 12 5 (1975) 741-753
43. Torres L., and Aguire L. Inductorless chua's circuit. Electron Lett 36 3 (2000) 1915-1916
44. Kennedy M. Robust op amp realization of chua's circuit. Frequenz 46 34 (1992) 66-80
45. Antoniou A. Realization of gyrators using opamps and their use in rc-active network synthesis. Proc IEE 116 11 (1969) 1838-1850
46. Khalil H.K. Nonlinear Systems. Third ed. (2002), Prentice Hall, Upper Saddle River, NJ
47. Horn R.A., and Johnson C.R. Matrix analysis (1985), Cambridge University Press, Cambridge, UK
48. Shil'nikov L.P. Chua's circuit: rigorous results and future problems. Int J Bifurcat Chaos 4 10 (1993) 489-519