Resumen de Hidden Dynamics in One-Dimensional Wave Equation

Xu Zhang, Liang Guo, Iram Hussan

• There are two kinds of chaotic attractors in ordinary differential equations, self-excited and hidden. However, there is no corresponding hidden attractors (or dynamics) in partial differential equations. In this article, a kind of one-dimensional wave equations with a certain kind of boundary conditions is provided, which can be regarded as the first partial differential equation with hidden dynamics. The coexistence of regular and chaotic dynamics (i.e., the dynamical behavior is by turns regular and complicated, or the oscillation is partly hidden and partly visible) can be observed, where the existence of chaotic dynamics is verified by the snap-back repeller theory. Further, three examples with numerical experiments are given to illustrate the theoretical results.