10 citations
4 papers
On a High-Precision Method for Studying Attractors of Dynamical Systems and Systems of Explosive Type
Alexander N. Pchelintsev
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…
On the Poisson Stability to Study a Fourth-Order Dynamical System with Quadratic Nonlinearities
Alexander N. Pchelintsev
This article discusses the search procedure for the Poincaré recurrences to classify solutions on an attractor of a fourth-order nonlinear dynamical system using a previously devel…
An Accurate Numerical Method and Algorithm for Constructing Solutions of Chaotic Systems
Alexander N. Pchelintsev
In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynam…
The harmonic balance method for finding approximate periodic solutions of the Lorenz system
Alexander N. Pchelintsev, Andrey A. Polunovskiy, Irina Yu. Yukhanova
We consider the harmonic balance method for finding approximate periodic solutions of the Lorenz system. When developing software that implements the described method, the math pac…