Anaslysys of dependence on numerical errors in the bifurcation process of dynamical system and development new adaptive numerical scheme

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04751
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Computational science
• Research Institution: Kanazawa University
• Principal Investigator: Hataue Itaru 金沢大学, 電子情報学系, 教授 (50218476)
• Co-Investigator(Kenkyū-buntansha): 長山 雅晴 北海道大学, 電子科学研究所, 教授 (20314289) ; 税所 康正 広島大学, 工学研究科, 准教授 (70195973)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: randomness / reaction-diffusion eq. / FitzHugh-Nagumo eq. / stability / van der Pol model

Outline of Final Research Achievements

The properties of several types of asymptotic solutions of one- and two-dimensional reaction-diffusion system with the FitzHugh-Nagumo model and the extended van der Pol oscillator model were studied. When several asymptotic solutions coexist in a parameter region around the bifurcation point, the dynamic locally connecting bistable solutions (d-LCBSs) which consists of two domains can be effectively obtained by developing the newly suggested preconstructed initial condition given by calculating with large random noises in the present study.
The relative stability levels of two stable uniform asymptotic solution patterns in the transition process from one pattern to another ones were evaluated by the amplitude of adding random noises. Furthermore, it was elucidated that the random noises affect the stability of boundary of the LCBS.

Free Research Field

Applied Mathematics