Real networks are frequently dynamic. Nevertheless, knowledge about analyzing algorithms and stochastic processes on dynamic networks is limited, compared to the wealth of knowledge on static networks. Therefore, dynamic network theoretical analyses have attracted much attention in network science and engineering. This article reviews random walks on dynamic network analysis, focusing on cover time. We also introduce the “collecting coupons with an increasing number of types,” from our recent work on random walks on dynamic graph analysis with an increasing number of vertices.
This survey reviews the numerical bifurcation analysis for dynamical systems and explains the pseudo-arclength continuation and detection and location methods for a bifurcation point. Moreover, locating methods for periodic and homoclinic solutions of ordinary differential equations are described. As a more advanced topic, the parameterization method for locating a quasiperiodic closed invariant curve for discrete-time dynamical systems is discussed. Finally, an application of these methods to the numerical continuation of rippling rectangular waves for the modified Benney equation is introduced.