Foundations of Synergetics, Volume 1This 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. |
Other editions - View all
Foundations of Synergetics I: Distributed Active Systems Alexander S. Mikhailov Limited preview - 2012 |
Foundations of Synergetics I: Distributed Active Systems Alexander S. Mikhailov Limited preview - 2012 |
Common terms and phrases
activatory active medium agents amplitude approximation associative memory assume attraction basins Belousov-Zhabotinskii reaction bistable media Boltzmann machine cells cellular automata coefficients connections consider core corresponds curvature dependence derivatives described determined diffusion dissipative patterns distributed active systems dynamical system effect eigenvalue energy evolution excitable media excitation wave filament front function given Haken Hence 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 self-organization 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 transition trigger wave u₁ unstable variables vortex wave patterns wavefront wavenumber