Chaos controlling of extended nonlinear Liénard system based on the Melnikov theory

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.