Abstract
The chaotic behaviors of a particle in a triple well φ6 potential possessing both homoclinic and heteroclinic orbits under harmonic and Gaussian white noise excitations are discussed in detail. Following Melnikov theory, conditions for the existence of transverse intersection on the surface of homoclinic or heteroclinic orbits for triple potential well case are derived, which are complemented by the numerical simulations from which we show the bifurcation surfaces and the fractality of the basins of attraction. The results reveal that the threshold amplitude of harmonic excitation for onset of chaos will move downwards as the noise intensity increases, which is further verified by the top Lyapunov exponents of the original system. Thus the larger the noise intensity results in the more possible chaotic domain in parameter space. The effect of noise on Poincare maps is also investigated.
Original language | English |
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Pages (from-to) | 127-138 |
Number of pages | 12 |
Journal | Chaos, Solitons and Fractals |
Volume | 27 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2006 |