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The networks of globally coupled maps with a pacemaker have been introduced. We consider a generalization of the Kaneko model with a pacemaker represented by a single period-doubling element coupled unidirectionally with a set of other mutually coupled cells. We also investigate the dynamics of a system of two unidirectionally coupled elements, which manifests a special type of critical behaviour, known asbicriticality, at the point of simultaneous transition to chaos in both subsystems. Withdoi:10.1155/ddns/2006/74723 fatcat:d3gzzz6wpvborcghh5t6cjq4cq