{"title":"Accessibility and stabilization by infinite horizon optimal control with negative discounting","authors":"Fumihiko NAKAMURA","doi":"10.14492/hokmj/2021-551","DOIUrl":"https://doi.org/10.14492/hokmj/2021-551","url":null,"abstract":"The present paper investigates systems exhibiting two attractors, and we discuss the problem of steering the state from one attractor to the other attractor by our idea of associating with the stabilization problem an optimal control problem. We first formulate the steering problem and give partial answers for the problem in a two-dimensional case by using the ordinary differential equation based on the infinite horizon optimal control model with negative discounts. Furthermore, under some conditions, we verify that the phase space can be separated into some openly connected components depending on the asymptotic behavior of the orbit starting from initial points in their components. This classification of initial points suggests that the system enables robust stabilizable control. Moreover, we illustrate some numerical results for the control obtained by applying our focused system for the Bonhoeffer–Van der Pol model.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136204781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Certain Convexity Properties of Hurwitz-Lerch Zeta and Mittag-Leffler Functions","authors":"D. Bansal, R. K. Raina","doi":"10.14492/hokmj/2021-543","DOIUrl":"https://doi.org/10.14492/hokmj/2021-543","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48225472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On surjective homomorphisms from a configuration space group to a surface group","authors":"K. Sawada","doi":"10.14492/hokmj/2021-526","DOIUrl":"https://doi.org/10.14492/hokmj/2021-526","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42608374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A remark on the condition $bm{1/p = 1/p_1 + 1/p_2}$ for boundedness of bilinear pseudo-differential operators with exotic symbols","authors":"Tomoya Kato, Naoto Shida","doi":"10.14492/hokmj/2021-539","DOIUrl":"https://doi.org/10.14492/hokmj/2021-539","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66754184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the cofiniteness of local cohomology modules in dimension < 2","authors":"N. Hoang, Ngô Thị Ngoan","doi":"10.14492/hokmj/2020-428","DOIUrl":"https://doi.org/10.14492/hokmj/2020-428","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41361149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Tanno connection and the Chern-Moser connection, in almost CR-geometry","authors":"M. Nagase","doi":"10.14492/hokmj/2021-505","DOIUrl":"https://doi.org/10.14492/hokmj/2021-505","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45815002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Gauss-Bonnet type theorem for future directed fronts in hyperbolic 3-space and de Sitter 3-space","authors":"Cuilian Zhang, D. Pei","doi":"10.14492/hokmj/2020-419","DOIUrl":"https://doi.org/10.14492/hokmj/2020-419","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48255666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Local equivalence of some maximally symmetric rolling distributions and $SU(2)$ Pfaffian systems","authors":"Matthew Randall","doi":"10.14492/hokmj/2021-502","DOIUrl":"https://doi.org/10.14492/hokmj/2021-502","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42182679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}