Chaotic motion for the generalized KdV–Burgers equation with external perturbation

摘要

The bifurcation and chaos in the generalized KdV–Burgers equation under periodic perturbation are investigated numerically in some detail. It is shown that dynamical chaos can occur when we choose appropriately systematic parameters and initial conditions. Abundant bifurcation structures and different routes to chaos such as period-doubling and inverse period-doubling cascades, intermittent bifurcation and crisis are found by using bifurcation diagrams, Poincaré maps and phase portraits. To characterize the chaotic behavior of this system, the spectrum of the Lyapunov exponent and the Lyapunov dimension of the attractor are also employed.