Proposal and application of a useful bifurcation point detection method for various systems using evolutionary computation optimization methods

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K12138
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 61040:Soft computing-related
• Research Institution: Kagawa University
• Principal Investigator: Matsushita Haruna 香川大学, 創造工学部, 准教授 (00604539)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: 分岐点探索 / 分岐図 / 分岐解析 / 計算知能 / 力学系

Outline of Final Research Achievements

We extended and improved the nested-layer bifurcation point search strategy using swarm intelligence. First, the proposed method was extended to the detection of local bifurcation points in continuous dynamical systems. Furthermore, we extended it to piecewise smooth maps which are a mixture of continuous and discrete dynamical systems, and succeeded in detecting characteristic bifurcation points of that systems. At the same time, we investigated the problems of conventional methods and tried to improve the detection of bifurcation points that could not be detected correctly. Since all the proposed methods are non-gradient methods, they can be used to analyze systems that are difficult to apply with conventional gradient-based methods. Furthermore, since they do not require complicated preprocessing, they can be used by non-experts in bifurcation analysis and swarm intelligence. In other words, we have proposed an easy-to-use bifurcation point detection method for a variety of systems.

Free Research Field

計算知能

Academic Significance and Societal Importance of the Research Achievements

提案手法はいずれも非勾配法であることから、従来法では適用困難であった系の解析にも利用可能である。さらに、煩雑な前処理を必要としないため、分岐解析や群知能の専門家でなくとも利用可能である。つまり、様々なシステムを対象とする手軽な分岐点導出法を提案に成功した。これを利用することで、これまでは解析不可能であったシステムの知らざる現象を解明できる可能性がある。