A non-autonomous flow system with Plykin type attractor |
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Authors: | Sergey P Kuznetsov |
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Institution: | 1. Institute of Mathematics NASU, Tereshchenkivska st. 3, Kyiv 01601, Ukraine;2. Kyiv School of Economics, Dmytrivska st. 92–94, Kyiv 01135, Ukraine;3. Department of Economics, Society and Politics, University of Urbino, Via Saffi 42, Urbino 61029, Italy;4. Department of Economics, Northwestern University, 2001 Sheridan Road, Evanston, Illinois 60208, USA |
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Abstract: | A non-autonomous flow system is introduced with an attractor of Plykin type that may serve as a base for elaboration of real systems and devices demonstrating the structurally stable chaotic dynamics. The starting point is a map on a two-dimensional sphere, consisting of four stages of continuous geometrically evident transformations. The computations indicate that in a certain parameter range the map has a uniformly hyperbolic attractor. It may be represented on a plane by means of a stereographic projection. Accounting structural stability, a modification of the model is undertaken to obtain a set of two non-autonomous differential equations of the first order with smooth coefficients. As follows from computations, it has the Plykin type attractor in the Poincaré cross-section. |
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