Attractive target wave patterns in complex networks consisting of excitable nodes

This review describes the investigations of oscillatory complex networks consisting of excitable nodes,focusing on the target wave patterns or say the target wave attractors.A method of dominant phase advanced driving(DPAD) is introduced to reveal the dynamic structures in the networks supporting oscillations,such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks.The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns.Therefore,the center(say node A) and its driver(say node B) of a target wave can be used as a label,(A,B),of the given target pattern.The label can give a clue to conveniently retrieve,suppress,and control the target waves.Statistical investigations,both theoretically from the label analysis and numerically from direct simulations of network dynamics,show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large,and all these attractors can be labeled and easily controlled based on the information given by the labels.The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.