An Analysis Of The Hopf Bifurcation And Computer Simulation For One-dimensional Maxwell-type Nonlinear System

Main Article Content

Temur Jangveladze
Mikheil Gagoshidze

Abstract

One-dimensional nonlinear Maxwell-type system is considered. The initialboundary value problem with mixed type boundary conditions is discussed. It is proved that in some cases of nonlinearity there exists critical value of the boundary data ????, such that for a suffciently small positive values of ?? the steady state solution is linearly stable. But as ?? passes through a critical value ????, the stability changes and a Hopf bifurcation may takes place. The finite difference scheme is constructed. Results of numerical experiments with graphical illustrations are given.

Keywords:
Maxwell-type one-dimensional nonlinear system, stationary solution, linear stability, Hopf-type bifurcation, finite difference scheme, computer simulation
Published: Nov 21, 2021

Article Details

How to Cite
Jangveladze, T. ., & Gagoshidze, M. . (2021). An Analysis Of The Hopf Bifurcation And Computer Simulation For One-dimensional Maxwell-type Nonlinear System. Proceedings of Tskhum-Abkhazian Academy of Sciences, 21, 186–200. Retrieved from https://proceedings.taas.ge/index.php/taas/article/view/5461
Section
Applied Mathematics
Author Biographies

Temur Jangveladze, Georgian Technical University (GTU)

Doctor of Physical and Mathematical Sciences

Chief Scientific Researcher

Head of Department of Partial Differential Equations, I.Vekua Institute of Applied Mathematics of I.Javakhishvili Tbilisi State University

Professor, Georgian Technical University, Department of Mathematics

E-mail: tjangv@yahoo.com

Mikheil Gagoshidze, Iv. Javakhishvili Tbilisi State University

Ph.D. Academic Degree in Informatics

Scientific Researcher, I.Vekua Institute of Applied Mathematics of I.Javakhishvili Tbilisi State University

E-mail: mishaGagoshidze@gmail.com,
mikheil.Gagoshidze@tsu.ge