{"title":"非双曲慢-快系统的极限周期和临界期","authors":"Peter De Maesschalck , Joan Torregrosa","doi":"10.1016/j.jde.2025.113307","DOIUrl":null,"url":null,"abstract":"<div><div>By considering planar slow-fast systems with a curve of double singular points, we obtain lower bounds on the number of limit cycles of polynomial systems surrounding a single singular point, as well as on the number of critical periods in one annulus of periodic orbits. In some circumstances, orbits of such slow-fast systems do not exhibit the typical slow-fast behavior but instead follow a hit-and-run pattern: they quickly move toward the critical curve, pause briefly there, and then continue their path.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113307"},"PeriodicalIF":2.3000,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Limit cycles and critical periods with non-hyperbolic slow-fast systems\",\"authors\":\"Peter De Maesschalck , Joan Torregrosa\",\"doi\":\"10.1016/j.jde.2025.113307\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>By considering planar slow-fast systems with a curve of double singular points, we obtain lower bounds on the number of limit cycles of polynomial systems surrounding a single singular point, as well as on the number of critical periods in one annulus of periodic orbits. In some circumstances, orbits of such slow-fast systems do not exhibit the typical slow-fast behavior but instead follow a hit-and-run pattern: they quickly move toward the critical curve, pause briefly there, and then continue their path.</div></div>\",\"PeriodicalId\":15623,\"journal\":{\"name\":\"Journal of Differential Equations\",\"volume\":\"433 \",\"pages\":\"Article 113307\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2025-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022039625003341\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625003341","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Limit cycles and critical periods with non-hyperbolic slow-fast systems
By considering planar slow-fast systems with a curve of double singular points, we obtain lower bounds on the number of limit cycles of polynomial systems surrounding a single singular point, as well as on the number of critical periods in one annulus of periodic orbits. In some circumstances, orbits of such slow-fast systems do not exhibit the typical slow-fast behavior but instead follow a hit-and-run pattern: they quickly move toward the critical curve, pause briefly there, and then continue their path.
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics