力学系の計算機シミュレーション(<特集>力学系理論-応用数理における新しい展開)

概要

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In dynamical systems, the geometrical approach with computer simulation technique is useful to investigate nonlinear phenomena, such as properties of invariant set, local and global bifurcations, generation of chaotic state, and so on. We present an introduction to methods for constructing computational algorithms on dynamical systems described by ordinary differential equations. Some effective algorithms derived from the geometric and numeric methods to determine bifurcation values are concretely summarized. Namely, we give elementary methods for obtaining parameter values of codimension-one and -two bifurcations of periodic solutions and appearance of separatrix loop in autonomous system. We also mention some of the most popular package programs developed to support the analysis of dynamical systems.
1997-12-15