mechanism underlying these new types of oscillations and the e ff ective methods to control and regulate the oscillatory dynamics have far from been clear. In this paper we study the oscillatory behaviors of self-sustained target waves in small-world networks of excitable nodes. We proposed a novel method of dominant phase-advanced driving to reveal the suc- cessive driving structures supporting the self-sustained oscillations, based on the known network structure and oscillation data. In these structures oscillation sources and wave propagation pathways are explored explicitly, which are otherwise deeply hidden in randomly distributed target groups. Based on the struc- ture we are able to e ff ectively control and regulate the oscillations of the excitable networks by suitably manipulating very few long-range links. The paper is arranged as follows. In Sec. II we describe the basic idea and the operating procedure of dominant phase-advanced driving (DPAD) method. Then we explain based on the graph theory why this method can reveal the essential structure generating self-sustained oscillations from complicated oscillatory patterns of complex networks. In Sec. III we study a model of small-world networks consisting of excitable nodes. We reveal both oscillatory patterns of spiral waves and multiple-target waves. The mechanism of the former case is well known – spiral wave tips serve as the os cillation generators. In the latter case, we apply the DPAD method and explicitly explore the wave source and the wave propagation pathways. In Sec. IV we show how to e ff ectively control self-sustained target patterns based on the above understanding. In Sec. V we analyze the conditions for the applications of the DPAD method, and show how this method can provide useful understanding even if partial necessary information are not available. The last section gives brief discussion on the results and the significance ofour method. Considering a general network graph G ( V , E ) with V representing a set of N nodes and E being a set of M interactions (i.e., couplings). Dynamic variables are associated to each node, and these variables obey well defined coupled ordinary di ff erential equations (ODEs). Each node is nonoscillatory individually while the entire complex networks are periodically oscillatory. It is well known that a necessary condition for this type of oscillatory networks is that there must exist some interacting loops. For any connected network with N nodes and M interactions, the number of fundamental cycles is M − N + 1 [20]. And the number of topological cycles serving as the candidates of source loops are 2 M − N + $^{1}$− 1, which is huge in the case M ≫ N (this is so for most of practical networks). Cycles are referred to as loops in our paper for simplicity. In this section we will propose an e ff ective method to identify the key dynamic loops generating the oscillations from the large number of topological loops. II. ANALYZING SELF-SUSTAINED OSCILLATION OF COMPLEX NETWORKS BY USING DPAD METHOD 2