7 these sources, all other target centers cease to emit waves successively due to the successive annihilations of their driving waves. Finally, the whole pattern with all waves generated by a large numbers of target centers evolves to the homogeneous rest state. Similar control e ff ects are observed for other self-sustained target patterns. When any single long-range link in the source loop is discarded, the given oscillation of the whole system is destroyed completely, and the system either evolves to the homogeneous rest state, or develops into an entirely di ff erent oscillatory structure due to the reconstruction of a di ff erent new source loop. It is really striking that by discarding only a single L-RC link among 2 × 10 4 local couplings and 150 L-RCs we can essentially change the dynamics of the whole pattern formation. This can never happen for spiral waves. It is emphasized that the self-sustained target waves are robust against random changes of the coupling structure. For instance, the main structure of pattern Fig. 2(c) is not considerably changed if we discard all L-RCs except the 9 relevant L-RCs shown in Fig. 2(c). A snapshot of pattern after discarding such 141 L-RCs are shown in Fig. 4(c). Fig. 4(d) shows the asymptotic pattern when we discard all 148 L-RCs in Fig. 2(c) except the 2 L-RCs A $^{′}$$_{1}$B$_{1}$ and B $^{′}$$_{1}$A$_{1}$ in the source loop. The oscillation continues just with these two long-range links. The comparison of Fig. 4(d) (discarding 148 L-RCs and keeping only the two L-RCs in the source loop) with Fig. 4(b) (discarding only a single L-RC in the source loop) is really striking. In the above applications of the DPAD method, we required full and precise knowledge on the interaction structures of networks and the variable data of oscillatory nodes. In realistic cases, the information is often not complete, it is thus necessary to consider the robustness of our approach in these practical situations. First, in practical experiments the measured data are often not precise, i.e., we should consider noisy data. In these cases, our method has an advantage of robustness. The validity of the DPAD method does not rely on precise values of data measurements, but depend on the topological orders of data, such as phase-advanced or phase-delayed interactions and dominant or nondominant drivings. These topological orders can often be correctly explored when the data measurements have certain small errors. Moreover, for periodic oscillations we may reduce some random measurement errors by averaging the data in su ffi ciently long intervals by making optimal tradeo ff between the precision and the measurement expense. Those treatments are applicable when the errors are relative small. If the errors are large, the methods may no longer work. Now we focus on the second and the most important problem: the robustness of the DPAD method against the incompleteness of information. Another promising advantage of our method is that the pathways of TFL V. ROBUSTNESS OF APPLICATIONS OF THE DPAD METHOD