Chaos analysis for a class of hyperbolic equations with nonlinear boundary conditions

ABSTRACT

A system governed by a one-dimensional hyperbolic equation with a mixing transport term and both ends being general nonlinear boundary conditions is considered in this paper. By using the snap-back repeller theory, we rigorously prove that the system is chaotic in the sense of both Devaney and Li-Yorke when the system parameters satisfy certain conditions. Finally, numerical simulations are further presented to illustrate the theoretical results.

KEYWORDS:

• Chaos
• snap-back repeller theory
• hyperbolic equation
• nonlinear boundary condition

2010 MATH SUBJECT CLASSIFICATIONS:

• 34C28
• 35L05

Acknowledgments

The authors are very grateful to the editor and anonymous referees for their valuable comments which led to a great improvement of the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

Xiang was partially supported by the NSF of China (11901091) and NSF of Guangdong Province (2020A151501339). C.Wu was supported by the NSF of China [no. 11401096] NSF of Guangdong Province (2019A1515011648) and the research fund of Foshan University.