Bifurcations of periodic orbits and chaos in damped and driven morse oscillator

Abstract

Damped and driven Morse oscillator is investigated in detail. The existence and the bifurcations of harmonics, second-order and third-order subharmonics, second-order and third-order superharmonics are given by using second-order averaging method. The numerical simulations including bifurcation diagrams in three- and two-dimensional spaces, maximum Lyapunov exponents, phase portraits, poincaré map, exhibit the complicated dynamical behaviors. We show the period-doubling and reverse period-doubling routes to chaos, the onset of chaos, reverse period-6 bubble, period-4 bubble, period-one orbit suddenly switching to an invariant torus, chaotic regions with invariant torus or with complicated periodic windows, or with interior crisis, nice chaotic attractors, non-attracting chaotic set, and a new type of non-chaotic attractors. Moreover, the influence of initial conditions on the dynamical behavior is considered. Combining the existing results of Wiggins et al. with the new results reported in this paper, a more complete description of the system is now obtained.