It was observed in experiments by Freeman that a rabbit olfactory bulb EEG is with limit cycle if an odorant is familiar,and it transforms to near-limit cycle chaos otherwise.Watanabe observes that chaos increases the memory capacity.Breakspear and Terry reported the detection of generalized synchronization between different brain regions by means of electroencephalogram signals.Inspired by the phenomena,we have developed chaotic neural network chains.New terminology such as replication of chaos,entrainment by chaos,attraction of chaos by dissipative systems,attraction of chaotic cycles are used for the description of our research.