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This volume is devoted to the presentation of the main contributions to the workshop ‘‘From oscillations to excitability: A case study in spatially extended systems,’’ organized by the authors in Nice in June 1993. It gives an overview of the current research on spatiotemporal patterns in a wide range of systems that display self‐oscillatory or excitable behavior. It tries to give a better understanding of the transition from the oscillatory to the excitable regime and of its effect on the properties of spiral waves, and to fill the gap between the theories and concepts used to describe both regimes in the so‐called ‘‘active media.’’

The early stages of the spontaneous desynchronization of chemical oscillations of the limit cycle type in a two‐dimensional medium are investigated. It is shown in the framework of a reaction‐diffusion kinetics that the behavior of the system is governed by the phase dynamics. Target patterns are radiated from centers which are spontaneously emitted by the system. They have various characteristic frequencies which are always larger than the frequency of the bulk oscillations. The statistical distribution of these centers is shown to depend on the wavelength of the corresponding waves and on the parameters of the limit cycle. Rotating spiral waves which correspond to vortexlike phase fluctuations have a vanishingly small probability and have to be initiated.

The nucleation of persistent slip bands in stressed materials is described as a cooperative phenomenon for dislocation populations. It is the competition between their mobility and their nonlinear interactions (creation, annihilation, and pinning) which causes the instability of uniform dislocation distributions versus inhomogeneous ones and leads to the formation and persistence of dislocation patterns.