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

被引：2
作者：
Pchelintsev, Alexander N. [1 ]
机构：
[1] Tambov State Tech Univ, Dept Higher Math, Ul Sovetskaya 106, Tambov 392000, Russia
来源：
MATHEMATICS | 2022年 / 10卷 / 08期
关键词：
attractor; high-precision calculations; power series; asymptote; population explosion model; piecewise smooth system; the Chua system; the number pi; systems with hysteresis; ADOMIAN DECOMPOSITION METHOD; ACCURATE NUMERICAL-METHOD; EQUATIONS;
D O I：
10.3390/math10081207
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 righthand 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.
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页数：12
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