TY - JOUR

T1 - The wavelet transform method applied to a coupled chaotic system with asymmetric coupling schemes

AU - Jonq, Juang

AU - Li, Chin Lung

PY - 2013/10

Y1 - 2013/10

N2 - The wavelet transform method originated by Wei et al. (2002) [19] is an effective tool for enhancing the transverse stability of the synchronous manifold of a coupled chaotic system. Much of the theoretical study on this matter is centered on networks that are symmetrically coupled. However, in real applications, the coupling topology of a network is often asymmetric; see Belykh et al. (2006) [23,24], Chavez et al. (2005) [25], Hwang et al. (2005) [26], Juang et al. (2007) [17], and Wu (2003) [13]. In this work, a certain type of asymmetric sparse connection topology for networks of coupled chaotic systems is presented. Moreover, our work here represents the first step in understanding how to actually control the stability of global synchronization from dynamical chaos for asymmetrically connected networks of coupled chaotic systems via the wavelet transform method. In particular, we obtain the following results. First, it is shown that the lower bound for achieving synchrony of the coupled chaotic system with the wavelet transform method is independent of the number of nodes. Second, we demonstrate that the wavelet transform method as applied to networks of coupled chaotic systems is even more effective and controllable for asymmetric coupling schemes as compared to the symmetric cases.

AB - The wavelet transform method originated by Wei et al. (2002) [19] is an effective tool for enhancing the transverse stability of the synchronous manifold of a coupled chaotic system. Much of the theoretical study on this matter is centered on networks that are symmetrically coupled. However, in real applications, the coupling topology of a network is often asymmetric; see Belykh et al. (2006) [23,24], Chavez et al. (2005) [25], Hwang et al. (2005) [26], Juang et al. (2007) [17], and Wu (2003) [13]. In this work, a certain type of asymmetric sparse connection topology for networks of coupled chaotic systems is presented. Moreover, our work here represents the first step in understanding how to actually control the stability of global synchronization from dynamical chaos for asymmetrically connected networks of coupled chaotic systems via the wavelet transform method. In particular, we obtain the following results. First, it is shown that the lower bound for achieving synchrony of the coupled chaotic system with the wavelet transform method is independent of the number of nodes. Second, we demonstrate that the wavelet transform method as applied to networks of coupled chaotic systems is even more effective and controllable for asymmetric coupling schemes as compared to the symmetric cases.

KW - Asymmetric

KW - Controlling chaos

KW - Coupled chaotic system

KW - Synchronization

KW - Wavelet transform method

UR - http://www.scopus.com/inward/record.url?scp=84886952239&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2013.04.013

DO - 10.1016/j.aml.2013.04.013

M3 - Article

AN - SCOPUS:84886952239

SN - 0893-9659

VL - 26

SP - 984

EP - 990

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 10

ER -