Perturbations and Hopf bifurcation of the planar discontinuous dynamical system

Date

2005-01-01

Author

Akhmet, Marat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

49
views

0
downloads

The objective of the paper is to obtain results on the behavior of a specific plane discontinuous dynamical system in the neighbourhood of the singular point. A new technique of investigation is presented. Conditions for existence of the foci and centres are proposed. The focus-centre problem and Hopf bifurcation are considered. Appropriate examples are given to ilustrate the bifurcation theorem.

Subject Keywords

Planar dynamical systems, Discontinuous systems, Focus, Stability, Hopf bifurcation, Centre

URI

https://hdl.handle.net/11511/43612

Journal

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

DOI

https://doi.org/10.1016/j.na.2004.08.029

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Discontinuous Galerkin finite element methods with shock-capturing for nonlinear convection dominated models Yücel, Hamdullah; BENNER, Peter (2013-11-11) In this paper, convection-diffusion-reaction models with nonlinear reaction mechanisms, which are typical problems of chemical systems, are studied by using the upwind symmetric interior penalty Galerkin (SIPG) method. The local spurious oscillations are minimized by adding an artificial viscosity diffusion term to the original equations. A discontinuity sensor is used to detect the layers where unphysical oscillations occur. Finally, the proposed method is tested on various single- and multi-component prob...
Time Constrained Temporal Logic Control of Multi Affine Systems Aydın Göl, Ebru (2012-01-01) In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multiaffine systems and specifications given as syntactically co-safe linear temporal logic formulas over rectangular regions in the state space. The proposed algorithm is based on the estimation of time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition sys...
Discontinuous dynamics with grazing points Akhmet, Marat (2016-09-01) Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of solutions are thoroughly analyzed. A variational system around a grazing solution which depends on near solutions is constructed. Orbital stability of grazing cycles is examined by linearization. Small parameter method is extended for analysis of grazing orbits, and bifurcation of cycles is observed in an example. Linearization around an equilibrium grazing point ...
Acceleration of line of sight analysis algorithms with parallel programming Yılmaz, Gökhan; Sürer, Elif; Temizel, Alptekin (null; 2017-11-23) Line of sight (LOS) analysis is a set of methods and algorithms to determine the visible points in a terrain with reference to a specific observer point. This analysis is used in simulations, Geographic Information System (GIS) applications and games. For this reason, it is important to have a capability to get results quickly and facilitate analysis in such a way that the interaction with the changing reference points is possible. Van Kreveld, R2 and R3 are the most frequently used algorithms in line of si...
Expectation propagation for state estimation with discrete-valued hidden random variables Sarıtaş, Elif; Orguner, Umut; Department of Electrical and Electronics Engineering (2023-2-21) In this thesis, the expectation propagation (EP) approach of Minka is considered for the estimation problems in dynamical systems with discrete hidden random variables where optimal posteriors are usually intractable. The concept of context adjustment is introduced to avoid/alleviate indefinite covariance problems encountered in standard EP implementations in a systematic way. Additionally, the moment projection (Mprojection) problem involving pseudo-Gaussian likelihoods as factors is solved to be used in t...

Citation Formats

M. Akhmet, “Perturbations and Hopf bifurcation of the planar discontinuous dynamical system,” NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, pp. 163–178, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43612.