Bulletin of the Japan Society for Industrial and Applied Mathematics
Online ISSN : 2432-1982
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Volume 32, Issue 1
Displaying 1-11 of 11 articles from this issue
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  • Random Walks on Dynamic Graphs
    Shuji Kijima, Nobutaka Shimizu, Takeharu Shiraga
    2022 Volume 32 Issue 1 Pages 5-15
    Published: March 25, 2022
    Released on J-STAGE: June 30, 2022
    DOIhttps://doi.org/10.11540/bjsiam.32.1_5
    JOURNAL FREE ACCESS
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    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.

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  • Numerical Bifurcation Analysis for Dynamical Systems
    Tomoyuki Miyaji
    2022 Volume 32 Issue 1 Pages 16-26
    Published: March 25, 2022
    Released on J-STAGE: June 30, 2022
    DOIhttps://doi.org/10.11540/bjsiam.32.1_16
    JOURNAL FREE ACCESS
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    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.

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