Duck Factory on the Two-Torus: Multiple Canard Cycles Without Geometric Constraints
| Autor: | Ilya Schurov, Nikita Solodovnikov |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
0209 industrial biotechnology
Numerical Analysis Control and Optimization Algebra and Number Theory Mathematical analysis Torus Dynamical Systems (math.DS) 02 engineering and technology 01 natural sciences 010101 applied mathematics 020901 industrial engineering & automation Integer 34E17 Control and Systems Engineering Limit cycle Bounded function FOS: Mathematics Limit (mathematics) Mathematics - Dynamical Systems 0101 mathematics Rotation (mathematics) Rotation number Mathematics Poincaré map |
| Zdroj: | Journal of Dynamical and Control Systems. 23:481-498 |
| ISSN: | 1573-8698 1079-2724 |
| DOI: | 10.1007/s10883-016-9335-6 |
| Popis: | Slow-fast systems on the two-torus are studied. As it was shown before, canard cycles are generic in such systems, which is in drastic contrast with the planar case. It is known that if the rotation number of the Poincare map is integer and the slow curve is connected, the number of canard limit cycles is bounded from above by the number of fold points of the slow curve. In the present paper it is proved that there are no such geometric constraints for non-integer rotation numbers: it is possible to construct generic system with as simple as possible slow curve and arbitrary many limit cycles. Comment: 20 pages, 4 figures; proof is drastically simplified comparing to previous revision |
| Databáze: | OpenAIRE |
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