On a High-Precision Method for Studying Attractors of Dynamical Systems and Systems of Explosive Type

Alexander N. Pchelintsev
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Alexander N. Pchelintsev: Department of Higher Mathematics, Tambov State Technical University, ul. Sovetskaya 106, 392000 Tambov, Russia

Mathematics, 2022, vol. 10, issue 8, 1-12

Abstract: The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical asymptotes of solutions of systems of explosive type. A special case of such systems is the population explosion model. A theorem on the existence of asymptotes is proved. The extension of the numerical method for piecewise smooth systems is described using the Chua system as an example, as well as systems with hysteresis.

Keywords: attractor; high-precision calculations; power series; asymptote; population explosion model; piecewise smooth system; the Chua system; the number ?; systems with hysteresis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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