Global isochrons of a planar system near a phaseless set with saddle equilibria
| Autor: | Hinke M. Osinga, James Hannam, Bernd Krauskopf |
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| Rok vydání: | 2016 |
| Předmět: |
0301 basic medicine
Isochron Physics Compactification (physics) Mathematical analysis General Physics and Astronomy 01 natural sciences 010305 fluids & plasmas 03 medical and health sciences symbols.namesake Continuation 030104 developmental biology Planar Ordinary differential equation Quantum mechanics 0103 physical sciences Poincaré conjecture symbols Initial value problem General Materials Science Physical and Theoretical Chemistry Saddle |
| Zdroj: | The European Physical Journal Special Topics. 225:2645-2654 |
| ISSN: | 1951-6401 1951-6355 |
| DOI: | 10.1140/epjst/e2016-60072-4 |
| Popis: | Given an attracting periodic orbit of a system of ordinary differential equations, one can assign an asymptotic phase to any initial condition that approaches such a periodic orbit. All initial conditions with the same asymptotic phase lie on what is known as an isochron. Isochrons foliate the basin of attraction, and may have intriguing geometric properties. We present here two cases of a planar vector field for which the basin boundary — also referred to as the phaseless set — contains saddle equilibria and their stable manifolds. A continuation-based approach, in combination with Poincare compactification when the basin is unbounded, allows us to compute isochrons accurately and visualise them as smooth curves to clarify their overall geometry. |
| Databáze: | OpenAIRE |
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