Effect of bounded noise on chaotic motion of a triple-well potential system

The chaotic behavior of Duffing oscillator possessing both homoclinic and heteroclinic orbits and subjected to harmonic and bounded noise excitations is investigated. By means of the random Melnikov technique together with associated mean-square criterion, necessary conditions for onset of chaos resulting from homoclinic or heteroclinic bifurcation are derived semi-analytically. The results reveal that for larger noise intensity the threshold amplitude of bounded noise for onset of chaos will move upward as the noise intensity increases, which is further verified by the top Lyapunov exponents of the system. Thus the larger the noise intensity results in the less possible chaotic domain in parameter space. The effects of bounded noise on Poincare maps of the system responses are also discussed, together with the numerical simulation of the top Lyapunov exponents