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.

中文翻译：

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一类具有非线性边界条件的双曲方程的混沌分析

摘要

本文考虑了一个由一维双曲方程控制的系统，该方程具有混合传输项，两端为一般非线性边界条件。通过使用回弹排斥理论，我们严格证明了当系统参数满足一定条件时，系统在 Devaney 和 Li-Yorke 意义上都是混沌的。最后，进一步提出数值模拟来说明理论结果。