TY - JOUR
T1 - Chaos controlling of extended nonlinear Liénard system based on the Melnikov theory
AU - Li, Ruihong
AU - Xu, Wei
AU - Li, Shuang
PY - 2006/7/15
Y1 - 2006/7/15
N2 - Chaos control may have a dual function, to generate chaos or to suppress it. By the Melnikov theory, two criterions of controlling chaos for a class of nonlinear Liénard system are established. According to the criterions, we implement chaos control using non-feedback method. Two illustrative examples, a Duffing-Rayleigh oscillator imposed with a weak bounded noise control, and a Duffing-van der Pol oscillator subject to a harmonic parametric control are presented here to illustrate the validity of the criterions. To better support the results obtained above, some indicators are used, namely the Lyapunov exponent, phase portrait, Poincaré cross-section and time evolution. Both two methods lead to fully consistent results.
AB - Chaos control may have a dual function, to generate chaos or to suppress it. By the Melnikov theory, two criterions of controlling chaos for a class of nonlinear Liénard system are established. According to the criterions, we implement chaos control using non-feedback method. Two illustrative examples, a Duffing-Rayleigh oscillator imposed with a weak bounded noise control, and a Duffing-van der Pol oscillator subject to a harmonic parametric control are presented here to illustrate the validity of the criterions. To better support the results obtained above, some indicators are used, namely the Lyapunov exponent, phase portrait, Poincaré cross-section and time evolution. Both two methods lead to fully consistent results.
KW - Bounded noise
KW - Chaos control
KW - Liénard system
KW - Melnikov theory
KW - Non-feedback method
KW - The top Lyapunov exponent
UR - http://www.scopus.com/inward/record.url?scp=33746228073&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2005.11.057
DO - 10.1016/j.amc.2005.11.057
M3 - 文章
AN - SCOPUS:33746228073
SN - 0096-3003
VL - 178
SP - 405
EP - 414
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 2
ER -