Encyclopedia of Nonlinear Science

In 438 alphabetically arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others. Designed for students and new researchers, as well as established nonlinear scientists interested applying methods outside their own specialized areas, this is the definitive introductory reference to all aspects of nonlinear science. Key Features * The first major reference in this growing field * A one-stop resource for students and researchers from a variety of scientific areas * 438 authoritative entries written by an international team of leading specialists * Extensive cross-references guiding the reader to related topics * Over 460b/w and color illustrations illuminating aspects of nonlinear phenomena * Authoritative and up-to-date suggestions for further reading Also includes an 8-page color insert.

Selected Contents: Algorithmic complexity Ball lightning Biological evolution Boundary value problems Butterfly effect Cardiac arrhythmias and electrocardiogram Cellular automata Chaos vs. turbulence Controlling chaos Determinism Dynamical systems Emergence Fluid dynamics Fractals Game of life Laboratory models of nonlinear waves Monte-Carlo methods Multidimensional solitons Neural network models Nonequilibrium statistical mechanics Nonlinear optics Nonlinear Schrödinger equations Nonlinear toys Numerical methods Order from chaos Partial differential equations, nonlinear Period doubling Perturbation theory Population dynamics Quantum chaos Random matrix theory Reaction diffusion systems Sandpile model Spatio-temporal chaos Sine--Gordon (SG) equation Stochastic analyses of neural systems Symmetry groups Tacoma Narrows Bridge collapse Threshold phenomena Universality Vortex dominated flows Wave stability and instability