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.