{"title":"Cellular automaton obtained by the tropical discretization from the competitive diffusion equation","authors":"M. Murata","doi":"10.14495/jsiaml.14.61","DOIUrl":"https://doi.org/10.14495/jsiaml.14.61","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88962326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Error analysis of the truncated Taylor series expansion method for computing matrix exponential","authors":"Yusaku Yamamoto, Shuhei Kudo, T. Hoshi","doi":"10.14495/jsiaml.14.147","DOIUrl":"https://doi.org/10.14495/jsiaml.14.147","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80538951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Causal inference for empirical dynamical systems based on persistent homology","authors":"Hiroaki Bando, S. Kaji, Takaharu Yaguchi","doi":"10.14495/jsiaml.14.69","DOIUrl":"https://doi.org/10.14495/jsiaml.14.69","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73015408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Explicit construction of the square-root Vélu's formula on Edwards curves","authors":"S. Takahashi, Hiroshi Onuki, T. Takagi","doi":"10.14495/jsiaml.14.108","DOIUrl":"https://doi.org/10.14495/jsiaml.14.108","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77126452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Poincaré integral invariant and conserved quantity of Toda lattice systems","authors":"N. Sasa","doi":"10.14495/jsiaml.14.88","DOIUrl":"https://doi.org/10.14495/jsiaml.14.88","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73214970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Poincaré map approach to limit cycles of a simplified ultradiscrete Sel'kov model","authors":"S. Ohmori, Y. Yamazaki","doi":"10.14495/jsiaml.14.127","DOIUrl":"https://doi.org/10.14495/jsiaml.14.127","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78010111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Improvement of infinity norm estimations related to computer-assisted proofs of the Kolmogorov problem","authors":"Kenta Kobayashi, Yoshitaka Watanabe","doi":"10.14495/jsiaml.14.92","DOIUrl":"https://doi.org/10.14495/jsiaml.14.92","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85237883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In Terasaka et al. JSIAM Lett. (2020), we have proposed numerical verification methods to construct local Lyapunov functions around non-hyperbolic equilibria using non-linear transformations by up to third degree polynomials. In the present study, we extend these methods by proving that polynomials of an arbitrary degree can be applied to define the transformations and show an example problem where we have to use a fifth-degree polynomial to construct local Lyapunov functions.
{"title":"On numerical verification methods to construct local Lyapunov functions around non-hyperbolic equilibria for two-dimensional cases","authors":"Koki Nitta, Toshiki Sasaki, N. Yamamoto","doi":"10.14495/jsiaml.14.33","DOIUrl":"https://doi.org/10.14495/jsiaml.14.33","url":null,"abstract":"In Terasaka et al. JSIAM Lett. (2020), we have proposed numerical verification methods to construct local Lyapunov functions around non-hyperbolic equilibria using non-linear transformations by up to third degree polynomials. In the present study, we extend these methods by proving that polynomials of an arbitrary degree can be applied to define the transformations and show an example problem where we have to use a fifth-degree polynomial to construct local Lyapunov functions.","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82536229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Geometry of equilibrium curves and surfaces for discrete anisotropic energy","authors":"Yoshiki Jikumaru","doi":"10.14495/jsiaml.14.57","DOIUrl":"https://doi.org/10.14495/jsiaml.14.57","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85865820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Theoretical comparison of two conformal maps combined with the trapezoidal formula for the semi-infinite integral of exponentially decaying functions","authors":"Tomoaki Okayama, Katsuya Hirohata","doi":"10.14495/jsiaml.14.77","DOIUrl":"https://doi.org/10.14495/jsiaml.14.77","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85015049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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