Nonisotropic chaos induced by snap-back repellers and heteroclinic cycles of 3-D hyperbolic PDEs

This paper mainly studies the nonisotropic chaos of a class of 3-D linear hyperbolic PDE systems with superlinear boundary conditions. Using the snap-back repellers and heteroclinic cycles theories, the system with a linear and superlinear boundary condition is rigorously proved to be Devaney chaos, distributional chaos, and ω - chaos, and have positive entropy. The chaotic results are further extended to the system with two superlinear boundary conditions. Two examples illustrating the theoretical results are presented.