Boundary-Forced Spatial Chaos

We show that the presence of undulated boundaries can induce the formation of spatially chaotic, stationary, and stable structures in models as simple as the Fisher-Kolmogorov equation, which does not display any kind of chaos under common boundaries. 1 Introduction In the past few decades, considerable understanding of the phenomenon of temporal chaos in dynamical systems of few degrees of freedom has been achieved[1]. On the other hand, spatiotemporal chaos in extended dynamical systems with infinitely many degrees of freedom is currently under very active investigation[2]. It is remarkable however, that an area of problems laying somehow between the two extremes has not received so much attention, namely, purely spatial chaos as a stationary attractor of extended dynamical systems [3, 4, 5, 6, 7, 8, 9]. In the context of fluid dynamics, the existence of spatially chaotic, but temporally steady solutions would also fill a conceptual gap between two well-studied complex phenomena: ..