A new accurate numerical method of approximation of chaotic solutions of dynamical model equations with quadratic nonlinearities

•The numeric-analytical solution of differential equations.•Algorithm for constructing the trajectory arc.•Estimating the region of convergence of the power series.•The accuracy of the approximate chaotic solution.•Almost periodic function. In this article the authors describe the method of construc...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2016-10, Vol.91, p.108-114
Main Authors: Lozi, René, Pogonin, Vasiliy A., Pchelintsev, Alexander N.
Format: Article
Language:English
Subjects:
Almost periodic function
Attractor
Chen system
Dynamical Systems
Lorenz system
Mathematics
Nose–Hoover oscillator
Power series
Region of convergence
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Summary:•The numeric-analytical solution of differential equations.•Algorithm for constructing the trajectory arc.•Estimating the region of convergence of the power series.•The accuracy of the approximate chaotic solution.•Almost periodic function. In this article the authors describe the method of construction of approximate chaotic solutions of dynamical model equations with quadratic nonlinearities in a general form using a new accurate numerical method. Numerous systems of chaotic dynamical systems of this type are studied in modern literature. The authors find the region of convergence of the method and offer an algorithm of construction and several criteria to check the accuracy of the approximate chaotic solutions.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2016.05.010