Modified parallel nested-layer particle swarm optimization algorithm for fast bifurcation point detection and its software implementation

This paper reports on the development of straightforward software for bifurcation point detection in discrete-time dynamical systems with a fast and versatile algorithm. Nested -layer particle swarm optimization (NLPSO) is an effective general-purpose bifurcation point detection strategy. In contrast to traditional gradient-based methods, the NLPSO method does not require derivatives of the objective functions. Note that NLPSO can incur high time costs, and parallel computation is practical. The software reported in this study employs modified NLPSO that is optimized for parallel computing. The proposed algorithm is fast and easy to use with limited knowledge of bifurcation point detection, algorithms, or parallel computing techniques.