### Abstract

Spatio-temporal chaos the image of which is an ensemble of interacting topological defects arises in many physical systems where spatially periodic states break down: at Marangoni convection in a layer heated from below, at excitation of capillary ripples on the surface of a viscous layer (Faraday ripples), in a wake behind a streamlined cylinder, and in many other systems. When one half-plane occupied by a periodic structure contains a period more than the other, we speak about topological defects. Topological defects are a two-dimensional analog of boundary dislocations in solids. The difference is that a boundary dislocation occurs in solids when there is a semi-infinite layer of atoms embedded in a perfect crystal, whereas in periodic structures it arises when there is an additional period. In spite of pronounced differences in physical properties of the systems, dynamics of topological defects that are analogs of boundary dislocations in crystals has much in common. We demonstrate that with increasing supercriticality (amplitude of layer oscillations for Faraday ripples, temperature difference for thermoconvection, etc.) the defects increase in number and may form bound states, domain walls and other structures. An increase of supercriticality in such systems leads to the transition from a regular state to spatio-temporal chaos. Controlling chaos of topological defects is a most important task. We study this problem on an example of chaos of topological defects in Faraday ripples. We show that the motion of topological defects and the characteristics of chaos can be controlled by means of pump frequency modulation.