Wandering walk of chimera states in a continuous medium

The coexistence of coherent and incoherent domains in discrete coupled oscillators, chimera state, has been attracted the attention of the scientific community. Here we investigate the macroscopic dynamics of the continuous counterpart of this phenomenon. Based on a prototype model of pattern formation, we study a family of localized states. These localized solutions can be characterized by their sizes, and positions, and Yorke-Kaplan dimension. Chimera states in continuous media correspond to chaotic localized states. As a function of parameters and their size, the position of these chimera states can be bounded or unbounded. This allows us to classify these solutions as wandering or confined walk. The wandering walk is characterized by a chaotic motion with a truncated Gaussian distribution in its displacement as well as memory effects.