Nonisotropic spatiotemporal chaotic vibrations of the one-dimensional wave equation with a mixing transport term and general nonlinear boundary condition

Abstract

Nonisotropic spatiotemporal chaotic vibrations can happen for a linear wave equation with a mixing transport term on the unit interval and with a nonlinear van der Pol boundary condition at one end when the parameter(s) enters some regime [Chen et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, 535 (2002)]. In this paper, on the one hand, the equation with general nonlinear boundary conditions is considered. On the other hand, parameter range for the route to chaos is more precisely classified. The results obtained here generalize and sharpen those both in the above paper and the earlier work of [Li, L. L. and Huang, Y., J. Math. Anal. Appl. 361, 69 (2010)]. Two examples and their corresponding numerical simulations of chaotic space-time profiles are also illustrated.