A new characterization of nonisotropic chaotic vibrations of the one-dimensional linear wave equation with a van der Pol boundary condition

The one-dimensional linear wave equation with a van der Pol nonlinear boundary condition is one of the simplest models that may cause isotropic or nonisotropic chaotic vibrations (Trans. Amer. Math. Soc. 350 (1998) 4265–4311, Internat. J. Bifur. Chaos 8 (1998) 423–445, Internat. J. Bifur. Chaos 8 (1998) 447–470, J. Math. Phys. 39 (1998) 6459–6489, Internat. J. Bifur. Chaos 12 (2002) 535–559). In this paper, we characterize nonisotropic chaotic vibration by means of the total variation theory. We obtain the classification results on the growth of the total variation of the snapshots on the spatial interval in the long-time horizon with respect to two parameters entering different regimes in R2.  2003 Elsevier Inc. All rights reserved.