Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, P.R. China
Abstract:
The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied. It is
found that the mechanism for chaos is the transverse heteroclinic tori. The Poincaré map, the stable and the unstable manifolds
of the system under two incommensurate periodic forces were set up on a two-dimensional torus. Utilizing a global perturbation
technique of Melnikov the criterion for the transverse interaction of the stable and the unstable manifolds was given. The
system under more but finite incommensurate periodic forces was also studied. The Melnikov's global perturbation technique
was therefore generalized to higher dimensional systems. The region in parameter space where chaotic dynamics may occur was
given. It was also demonstrated that increasing the number of forcing frequencies will increase the area in parameter space
where chaotic behavior can occur.
Biographies: Lou Jing-jun (1976≈) Zhu Shi-jian