A non-autonomous flow system with Plykin type attractor

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.

9 pages, 4 figures

References in corpus (2)

• An example of physical system with hyperbolic attractor of Smale - Williams type
• Hyperbolic attractor in a system of coupled non-autonomous van der Pol oscillators: Numerical test for expanding and contracting cones

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• On the number of ergodic physical/SRB measures of singular-hyperbolic attracting sets
• Sensitivity computation of statistically stationary quantities in turbulent flows
• Parameter space arrangement of a model system nearby domain of existence of Plykin type attractor