Dynamics of self-organized delay adaptation

Adaptation of interaction delays is essential for the functioning of many n atural and technical systems. We introduce a novel framework for studying t he dynamics of delay adaptation in systems which optimize coincidence of in puts. For the important case of periodically modulated input we derive cond itions for the existence and stability of solutions which constrain th set of mechanisms for reliable delay adaptation. Using numerical examples we sh ow that our approach is applicable to more general than periodic input patt erns such as Poissonian point processes with coordinated rate fluctuations. [S0031 -9007(99)08395-7].