Spatiotemporal Dynamics Near the Turing-Hopf Bifurcation

During the last few decades, there develop greatly many theoretical results to describe the dynamics of pattern formation[149,354]. Noticeably, the type of instability remains the main reason for the variation of the spatiotemporal patterns. But when two or more instabilities coincide, system will behave more complicated patterns than patterns generated by sole instability. A prominent example is the Turing-Hopf bifurcation in which two instabilities break the spatial or temporal symmetry, compete and interact with each other, then lead to various patterns like mixed modes, bistability, and spatiotemporal chaos [208].