About Analytical Approximate Solutions of the Van der Pol Equation in the Complex Domain-Reference-Cited by-同舟云学术

About Analytical Approximate Solutions of the Van der Pol Equation in the Complex Domain

Published:2023-03-03 Issue:3 Volume:7 Page:228
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Orlov Victor¹^ORCID,Chichurin Alexander²^ORCID

Affiliation:

1. Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Yaroslavskoe Shosse, 26, 129337 Moscow, Russia

2. Institute of Mathematics, Informatics and Landscape Architecture, The John Paul II Catholic University of Lublin, ul. Konstantynów 1H, 20-708 Lublin, Poland

Abstract

In the article, the existence of solutions for the Van der Pol differential equation is proved, and the approximate structure of such solutions in the analyticity domain is obtained. In the proof, the majorant method was applied not to the right side of the differential equation, as per usual, but to the solution to the nonlinear differential equation under consideration. Results of the numerical study are presented.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/3/228/pdf

Reference21 articles.

1. To the Problem on Limit Cycle of the Van der Pol Generator in Relaxation Mode;Sudakov;Her. Bauman Mosc. State Tech. Univ. Ser. Instrum. Eng.,2013

2. Phenomenon of the Van der Pol Equation;Kuznetsov;Izv. VUZ,2014

3. Birkhoff, G., and Rota, G. (1991). Ordinary Differential Equations, Wiley. [4th ed.].

4. Kreyszig, E. (2006). Advanced Engineering Mathematics, Wiley. [9th ed.].

5. Wiggins, S. (2003). Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer. [2nd ed.].

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