Investigación

 

Chaotic synchronization of irregular complex network with hysteretic circuit-like oscillators in hamiltonian form and its application in private communications

 

E. Garza-González^a, C. Posadas-Castillo^a, A. Rodríguez-Liñan^a and C. Cruz-Hernández^b

 

^a Universidad Autónoma de Nuevo León, Av. Pedro de Alba s/n, Cd. Universitaria, C.P. 66451, San Nicolas de los Garza N.L., México. e-mail: egarza.ikaro@gmail.com; cornelio.posadascs@uanl.edu.mx; angel.rodriguezln@uanl.edu.mx

^b Scientific Research and Advanced Studies Center of Ensenada. e-mail: ccruz@cicese.mx

 

Received 25 August 2015;
accepted 30 October 2015

 

Abstract

In this paper, a study on chaotic synchronization of an irregular network is made. Synchronization is achieved by using a modified Hamiltonian approach in a bidirectional irregular arrayed network made of 20 chaotic oscillators. The chaotic oscillator used as example is the Hysteretic circuit. Afterwards the concept is used in chaotic encryption to send secured confidential analog information. As a result, an image is encrypted using additive chaotic encrytion with two channels.

Keywords: Chaotic synchronization; hysteretic circuit; generalized hamiltonian system; private communication; complex networks.

 

Resumen

En este trabajo, un estudio de la sincronización caótica de una red irregular es realizada. La sincronización es alcanzada al usar una modificación al enfoque Hamiltoniano sobre una red bidireccional irregular creada por 20 osciladores caoticos. El oscilador caótico usado como ejemplo es el circuito de Histeresis. Después, este concepto es usado en encriptamiento caótico para enviar informacion análoga confidencial de manera segura. Como resultado, una imagen es encriptada usando encriptamiento caótico aditivo de dos canales.

Palabras clave: Sincronización caótica; circuito de histeresis; sistema hamiltoniano generalizado; comunicaciones privadas; redes complejas.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgments

This work was supported by CONACYT, México under Research Grant No. 166654.

 

References

1. C. Cruz-Hernández, Nonlinear Dyn. Syst. Theory 4 (2004) 1.         [ Links ]

2. X. Wu, G. Chen, and J. Cai, Phys. D229 (2007) 52.         [ Links ]

3. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64 (1990) 821.         [ Links ]

4. K. M. Cuomo, A. V. Oppenheim, and S. H. Strogatz, IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 40 (1993) 626.         [ Links ]

5. P. Grigolini, P. Hamilton, J. Roberts, and B. J. West, Chaos, Solitons & Fractals 20 (2004) 1.         [ Links ]

6. P. Grigolini, P. Allegrini, and B. J. West, Chaos, Solitons & Fractals 34 (2007)3.         [ Links ]

7. M.E. Newman, Phys. Rev. E 64 (2001) 016131.         [ Links ]

8. S. Redner, EPJB 4 (1998) 131.         [ Links ]

9. J. Scott, Sociology 22 (1988) 109.         [ Links ]

10. J. Galaskiewicz and S. Wasserman, Sociological Methods & Research 22 (1993) 3.         [ Links ]

11 . J. Cohen, T. Jonsson, and S. R. Carpenter, Proc. Nat. Acad. Sc. 100 (2003) 1781.         [ Links ]

12. E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, and A.-L. Barabási, Science 297 (2002) 1551.         [ Links ]

13. J. White, E. Southgate, J. Thomson, and S. Brenner, Phil. Trans. R. Soc.Lond 314 (1986) 1.         [ Links ]

14. L. Kocarev, K. Halle, K. Eckert, L.O. Chua, and U. Parlitz, Int. J. Bifurc. Chaos 2 (1992) 709.         [ Links ]

15. L. Cardoza-Avendano et al., Rev. Mex. Fis 58 (2012) 472.         [ Links ]

16. J.L. Mata-Machuca, R. Martínez-Guerra, R. Aguilar-López, and C. Aguilar-Ibañez, Commun. Nonlinear Sci. Numer. Simulat. 17 (2012) 1706.         [ Links ]

17. R. Núñez-Pérez, Rev. Mex. Fis. 52 (2006) 464.         [ Links ]

18. C. Tao and G. Du, Int. J. Bifurc. Chaos 13 (2003) 2689.         [ Links ]

19. G. Pérez and H. A. Cerdeira, Phys. Rev. Lett. 74 (1995) 1970.         [ Links ]

20. A. Aguilar-Bustos and C. Cruz-Hernández, Chaos, Solitons & Fractals 41 (2009) 1301.         [ Links ]

21. J.-P. Goedgebuer, L. Larger, and H. Porte, Phys. Rev. Lett. 80 (1998) 2249.         [ Links ]

22. N. Smaoui, A. Karouma, and M. Zribi, Commun. Nonlinear Sci. Numer. Simulat. 16 (2011) 3279.         [ Links ]

23. J. Lu and G. Chen, Int. J. Bifurc. Chaos 16 (2006) 775.         [ Links ]

24. L. Gámez-Guzmán, C. Cruz-Hernández, R. López-Gutiérrez, and E. García-Guerrero, Rev. Mex. Fis 299 (2008) 54.         [ Links ]

25. Y. Tang and J. Fang, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 401.         [ Links ]

26. X. Wu, H. Wang, and H. Lu, Nonlinear. Anal. Real App. 13 (2012) 1441.         [ Links ]

27. A. Kiani-B, K. Fallahi, N. Pariz, and H. Leung, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009) 863.         [ Links ]

28. C. Cruz-Hernández, in Procs. of the IASTED on Circuits, Signal, and Systems (2002).         [ Links ]

29. D. López-Mancilla, C. Cruz-Hernández, and C. Posadas-Castillo, in Journal of Physics: Conference Series, 23 (IOPublishing, 2005) p. 267.         [ Links ]

30. C. Posadas-Castillo, E. Garza-González, D. Diaz-Romero, E. Alcorta-García, and C. Cruz-Hernández, J. Appl. Res. Technol. 12 (2014) 782.         [ Links ]

31. H. Sira-Ramirez and C. Cruz-Hernández, Int. J. Bifurc. Chaos 11 (2001) 1381.         [ Links ]

32. X. F. Wang, Int. J. Bifurc. Chaos 12 (2002) 885.         [ Links ]

33. S. Boccaletti, J. Kurths, G. Osipov, D. Valladares, and C. Zhou, Phys. Rep. 366 (2002) 1.         [ Links ]

34. J. Wang and Y. Zhang, Phys. Let. A 374 (2010) 1464.         [ Links ]