##
Neural Networks and Self-Organized Structures

**Neural networks**
are used in neurocomputing and software engineering
as modern fast algorithms for self-learning,
image recognition, pattern formation. Each node of a global
network has interactions and couplings with other nodes
that are described by a weighted sum function. The
integral contribution of all interactions defines
the state of each node in the next time instance.

Neural networks exhibit self-organizing structures
localized in a certain region of the network and
traveling or pulsating over time dynamics.
The structures serve as attractors in image processing
algorithms and resemble dissipative structures
(*autowaves*) of various biological models for
nerve pulses.

The structures are classified as
*static*, *stationary propagating*
and *periodically pulsating*. Fronts, pulses,
trains of fronts and pulses, periodic chains and
lattices of individual pulses can be constructed
and studied by means of bifurcation theory,
nonlinear dynamics analysis, and numerical algorithms.