Nonisotropic chaotic vibrations of a 2D hyperbolic PDE

Qiaomin Xiang; Qigui Yang

doi:10.1063/1.5139910

Nonisotropic chaotic vibrations of a 2D hyperbolic PDE

Chaos. 2020 Feb;30(2):023127. doi: 10.1063/1.5139910.

Authors

Qiaomin Xiang¹, Qigui Yang²

Affiliations

¹ School of Mathematics and Big Data, Foshan University, Foshan 528000, People's Republic of China.
² School of Mathematics, South China University of Technology, Guangzhou 510000, People's Republic of China.

PMID: 32113240
DOI: 10.1063/1.5139910

Abstract

Little seems to be known about the chaos of the two-dimensional (2D) hyperbolic partial differential equations (PDEs). The objective of this paper is to study the nonisotropic chaotic vibrations of a system governed by a 2D linear hyperbolic PDE with mixed derivative terms (MDTs) and a nonlinear boundary condition (NBC), where the interaction between MDTs and NBC causes the energy of such a system to rise and fall. The 2D hyperbolic system is proved to be topologically conjugate with the corresponding Riemann invariants, which are rigorously proved to be chaotic. Two numerical examples are carried out to demonstrate the theoretical results.