Open AccessInfluence of harmonic and bounded noise excitations on chaotic motion of Duffing oscillator with homoclinic and heteroclinic orbits
Author(s) -
Xiaoli Yang,
Xu Wei,
Sun Zhong-Kui
Publication year - 2006
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.55.1678
Subject(s) - homoclinic orbit , bounded function , physics , chaotic , lyapunov exponent , heteroclinic orbit , duffing equation , noise (video) , mathematical analysis , heteroclinic cycle , bifurcation , heteroclinic bifurcation , classical mechanics , mathematics , bifurcation theory , nonlinear system , quantum mechanics , computer science , image (mathematics) , artificial intelligence
In this paper, the influence of harmonic and bounded noise excitations on the chaotic motion of a double well Duffing oscillator possessing both homoclinic and heteroclinic orbits is investigated. The criteria for occurrence of transverse intersection on the surface of homoclinic and heteroclinic orbits are derived by Melnikov theory, and are complemented by numerical calculations which display the bifurcation surfaces and the fractality of the basins of attraction. The results imply that the threshold amplitude of bounded noise for the onset of chaos moves upwards as the noise intensity increases beyond a critical value, which is further verified by numerically calculating the top Lyapunov exponents of the original system. Then we come to the conclusion that larger noise intensity results in smaller possible chaotic domain in the parameter space. The influence of bounded noise on Poincaré maps of the system response is also discussed, which indicates that when the noise intensity is less than some critical value, larger noise intensity results in larger area which the map occupies in the phase plane.