Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 405-414 |
| Number of pages | 10 |
| Journal | Applied Mathematics and Computation |
| Volume | 178 |
| Issue number | 2 |
| DOIs | |
| State | Published - 15 Jul 2006 |
Keywords
- Bounded noise
- Chaos control
- Liénard system
- Melnikov theory
- Non-feedback method
- The top Lyapunov exponent
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