## Foundations of synergetics: Distributed active systemsThis textbook presents an introduction to the mathematical theory of cooperative behavior in active systems of various origin, both natural and artificial. This volume (the first of two) is devoted to the properties of regular self-organized patterns in distributed active systems. An analysis of pattern formation and self-supported wave propagation in active media is followed by a description of the properties of neural networks and their possible applications in the field of distributed analog information processing. The volume ends with a discussion of reproductive networks and evolutionary systems. Attention is focused on basic models which might appear in a wide range of applications. As illustrations, the author uses simplified examples borrowed from a variety of disciplines ranging from chemical and biological physics to market economics. |

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activatory active medium agents amplitude analog information processing approximation associative memory assume attraction basins Belousov-Zhabotinskii reaction bistable media Boltzmann machine cells cellular automata coefficients connections consider core corresponds critical nucleus curvature dependence derivatives described determined diffusion dissipative patterns distributed active systems dynamical system effect eigenvalue energy evolution excitable media excitation wave filament front function Ginzburg-Landau equation given Haken Hence hole hypercube inhibitor concentration initial conditions interactions interface layer minimal molecules neural networks neurons nonlinear oscillations oscillatory media output units pacemaker parameter Perceptron period phase dynamics population population densities possible problem propagation velocity properties prototype patterns pulse radius reaction region reproductive networks rotation frequency scroll ring sequence simulated annealing simulations small perturbations solution species spike spin spin glass spiral wave steady stored patterns Suppose synaptic matrix Synergetics temperature term topological charge total number trigger wave unstable variables vortex wave patterns wavefront wavenumber