On cycles and other geometric phenomena in phase portraits of some nonlinear dynamical systems. (English) Zbl 1348.34063
Rovenski, Vladimir (ed.) et al., Geometry and its applications. Selected papers based on the presentations at the 2nd international workshop on geometry and symbolic computation, Haifa, Israel, May 15–18, 2013. Cham: Springer (ISBN 978-3-319-04674-7/hbk; 978-3-319-04675-4/ebook). Springer Proceedings in Mathematics & Statistics 72, 225-233 (2014).
Summary: We show existence of cycles in some special nonlinear 4-D and 5-D dynamical systems and construct in their phase portraits invariant surfaces containing these cycles. In the 5D case, we demonstrate non-uniqueness of the cycles. Some possible mechanisms of this non-uniqueness are described as well.
For the entire collection see [Zbl 1290.53002].
For the entire collection see [Zbl 1290.53002].
MSC:
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 92D10 | Genetics and epigenetics |
| 37N25 | Dynamical systems in biology |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34C41 | Equivalence and asymptotic equivalence of ordinary differential equations |
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