Learning in synergetic systems for pattern recognition and associative action

Synergetic systems are in particular physical systems which can produce spatial or temporal patterns by means of the interaction of their individual parts. We show how such a system can be devised or even learn by itself to reproduce given patterns described by their probability distribution function. If an initial state close to one of the learned patterns is presented to such a system, it will pull the initial state into an attractor belonging to the learned state (pattern recognition via associative memory). Furthermore we show how such a system can be devised or can learn to perform any prescribed stationary continous Markov process. If a set of incomplete or partly incorrect initial data is offered to such a system, it may correct it and perform associative action.