Abstract
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.
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Acknowledgements
The authors are indebted to A.A.Akinshin, I.V.Golubyatnikov, A.E.Gutman, and V.A.Likhoshvai for useful discussions and helpful assistance. The work was supported by RFBF, grant 12-01-00074, and by interdisciplinary grant 80 of SB RAS.
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Gaidov, A.Y., Golubyatnikov, P.V. (2014). On Cycles and Other Geometric Phenomena in Phase Portraits of Some Nonlinear Dynamical Systems. In: Rovenski, V., Walczak, P. (eds) Geometry and its Applications. Springer Proceedings in Mathematics & Statistics, vol 72. Springer, Cham. https://doi.org/10.1007/978-3-319-04675-4_10
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DOI: https://doi.org/10.1007/978-3-319-04675-4_10
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