Remarks on homoclinic structure in Bogdanov-Takens map
| Autor: | Al Hdaibat, Bashir, Govaerts, W., van Kekem, D.L., Kuznetsov, Yu.A., Sub Mathematical Modeling, Mathematical Modeling |
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| Přispěvatelé: | Applied Analysis, Sub Mathematical Modeling, Mathematical Modeling, Dynamical Systems, Geometry & Mathematical Physics |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
NUMERICAL-ANALYSIS
Mathematics::Dynamical Systems Bogdanov-Takens map homoclinic asymptotic Structure (category theory) homoclinic intersections ZONE 01 natural sciences CONNECTING ORBITS 010305 fluids & plasmas 0103 physical sciences Homoclinic bifurcation Asymptotic formula DIFFEOMORPHISMS Homoclinic orbit 0101 mathematics Bogdanov–Takens map Bifurcation Mathematics Algebra and Number Theory BIFURCATION Applied Mathematics 010102 general mathematics Mathematical analysis n/a OA procedure Nonlinear Sciences::Chaotic Dynamics Mathematics and Statistics Flow (mathematics) Transversal (combinatorics) Bounded function MatContM POINT Analysis |
| Zdroj: | Journal of Difference Equations and Applications, 24(4), 575. Taylor and Francis Ltd. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS Journal of difference equations and applications, 24(4), 575-587. Taylor & Francis Journal of Difference Equations and Applications, 24, 575-587 |
| ISSN: | 1023-6198 1563-5120 |
| Popis: | It is known that in the Bogdanov–Takens map there exists a zone of transversal homoclinic intersections bounded by two curves of homoclinic tangencies. In this paper, we derive an improved asymptotic formula for the homoclinic parameter values of the BT map. We compare two methods to approximate the Bogdanov–Takens map by the time-1 flow of a vector-field, and find that they are equivalent. We show that it is essential to include the second-order terms w.r.t. the parameters to obtain a more accurate asymptotic for the homoclinic zone. We show how to use this new homoclinic asymptotic to compute branches of homoclinic tangencies in the BT map numerically, obtaining the whole homoclinic structure of the Bogdanov–Takens map. |
| Databáze: | OpenAIRE |
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