入れ子構造型粒子群最適化を用いた非線形力学系のNeimark-Sacker分岐点導出法について

抄録

This paper investigates the Neimark-Sacker bifurcation points derivation method using the nested-layer particle swarm optimization (NLPSO) in nonlinear dynamical systems. In nonlinear dynamical systems, Neimark-Sacker bifurcation occurs when a complex conjugate characteristic multiplier crosses the unit circle by changing the parameters. NLPSO is not only under no careful initial values and complex hand calculation but also the advantage of deriving bifurcation points regardless of the stability of the systems. In order to obtain the Neimark-Sacker bifurcation parameters by NLPSO, the characteristic multiplier of the objective function must be set to a complex number. This method derives the local bifurcation points such as Neimark-Sacker bifurcation, period-doubling bifurcation, and saddle-node bifurcation by changing only the declination of the characteristic multiplier without changing the objective function and algorithm. As an application example, we give the results of deriving Neimark-Sacker bifurcation points in two-dimensional discrete dynamical and non-autonomous systems.