Controlling of Chaos in the Driven Chua's Circuit

Abstract

The nonautonomous version of Chua's circuit can exhibit a wide variety of bifurcation routes to chaos. In this paper we explore the possibility of controlling chaos in this circuit by the addition of a second periodic signal for certain parametric choices.Of late, considerable efforts are being made to find effective ways of controlling chaos in nonlinear dynamical systems by means of various external and internal manipulations such as the adaptive control mechanism, 16,17 small parametric perturbation, 18 ' 19 addition of a second weak periodic force, 20 stabilizing unstable periodic orbits 21,22 and so on. In this connection, in the present study, we wish to investigate the influence of a second periodic signal on the nonautonomous Chua's circuit to find out whether this perturbation can eliminate chaos. Our study 463 Chua's Circuit: A Paradigm for Chaos Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/20/15. For personal use only.

Controlled Parameter Modulations in Secure Digital Signal Transmissions

“…This idea immediately motivated several researcher to use chaotic signal for secure communication purpose with the belief that it will be difficult for an intruder to decipher the transmitted message without the knowledge of the transmitting chaotic system, due to its extremely high sensitiveness to the initial conditions and parameter mismatches. As a result, a number of methods have been proposed for secure communication and cryptography [Hayes et al, 1993;Cuomo & Oppenheim, 1993;Murali & Lakshmanan, 1993a;Murali & Lakshmanan, 1993b;Kocarev & Parlitz,1995;Lakshmanan & Murali, 1996;Zhang et al, 1998;Baptista, 1998;He & Vaidya,1998;Wong et al, 2003;Kocarev et al, 2004;Bowong, 2004;Hua et al, 2005;Chee & Xu 2006] using chaotic signals. In particular, Cuomo and Oppenheim [Cuomo & Oppenheim, 1993] have suggested a very simple method for secure digital signal transmission using the property of the coupled chaotic systems that a small difference between the corresponding parameters in the drive and response systems will cause synchronization frustration in their dynamical variables.…”