Chaos induced by snap-back repellers in a n-dimensional wave network

In this paper, we consider the chaotic behavior of a $ n $-dimensional wave network with mixed partial derivative linear energy transport terms. The symmetric nonlinearities of van der Pol type are proposed at each wave equation boundary endpoint, which cause the energy of the wave equation to rise and fall within certain ranges. At the interconnected point of the wave network, the energy is injected into the system through an anti-damping velocity feedback. By applying the snap-back repeller theory, the gradient of the wave equations is proved to be chaotic in the sense of Li-Yorke. Numerical simulations are also presented to illustrate the theory.