2011 Volume 59 Pages 13-25
Spatially localized patterns are ubiquitous such as chemical blobs, discharge patterns, morphological spot, and binary convection cells. When they are moving in space, it is unavoidable that they collide each other, interact strongly and emit various outputs depending on incident angle and parameters. Moving localized spots in dissipative systems have their own internal hidden dynamics. Here "hidden" means that various types of instabilities are not visible when they are isolated, but those ones come out from the hidden state when they collide with each other or encounter defects when the propagating media is heterogeneous. They display rich dynamics such as rebound, annihilation, coalescence, and splitting through the collision process. A new approach is presented to clarify an underlying structure behind those dynamics. A key ingredient lies in a network of unstable solutions, which plays a crucial role to understand the input-output relation for collisional process. A remarkable thing is that there appears a time-periodic rotational motion as an output for the case of oblique collision. This approach is also useful to understand the dynamics of traveling spots in heterogeneous media.