PERTURBED BEHAVIOR FOR THE MODEL OF WAVE PROPAGATION IN A NONLINEAR DISPERSIVE NONCONSERVATIVE MEDIA
As a governing equation of wave propagation in a nonlinear, dispersive and dissipative media, KdV–Burgers type equation has received great attention. In this paper, the dynamical behavior of the generalized KdV–Burgers equation under a periodic perturbation is investigated numerically in 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 applying bifurcation diagrams, the Poincaré maps and phase portraits. To characterize chaotic behavior of this system, the spectrum of Lyapunov exponent and Lyapunov dimension of the attractor are also employed.