Autowaves. Self-organization

The paper presents experimental studies on the formation of spiral structures of heavy particles by the field of parametrically excited standing spiral waves. Particles move under the influence of the average currents field generated near the bottom in a viscous liquid by standing waves. The formation of structures has a threshold character and depends on the intensity of the field of standing waves. Formation of multi-armed structures revealed.

We numerically and analytically investigate two self-organized critical sandpile models with anisotropic dynamics of the activity propagation – Dhar–Ramaswamy and discrete Feder–Feder models. The full set of critical indices for these models is theoretically

Investigation of a set of amplitude equations, describing interaction of several modes which became unstable due to the wave bifurcation, is carried out. It is shown that as a result of competition between modes depending on the value of the parameter defining the strength of interaction only two regimes are possible: either quasi one-dimensional travelling waves (there exists only one nonzero mode) or standing waves (al the modes are nonzero).