Bifurcation in a 3D Hybrid system

Date

2010-07-01

Author

Akhmet, Marat
Turan, Mehmet

Metadata

Show full item record

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

Item Usage Stats

16
views

0
downloads

In this paper, we study a 3 dimensional Hybrid system which involves a switching mechanism such that at the moment of switching the differential equation that governs the mode] is changing. We first show that there is a center manifold and based on the results in [2] we show that the system under investigation has a Hopf bifurcation. An appropriate example is constructed to illustrate the theory. © Dynamic Publishers, Inc.

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79551613544&origin=inward
https://hdl.handle.net/11511/99231

Journal

Communications in Applied Analysis

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Oscillation criteria for third-order nonlinear functional differential equations AKTAŞ, MUSTAFA FAHRİ; Tiryaki, A.; Zafer, Ağacık (Elsevier BV, 2010-07-01) In this work, we are concerned with oscillation of third-order nonlinear functional differential equations of the form
Bifurcation of a non-smooth planar limit cycle from a vertex Akhmet, Marat (2009-12-15) We investigate non-smooth planar systems of differential equations with discontinuous right-hand sides. Discontinuity sets intersect at a vertex, and are of quasilinear nature. By means of the B-equivalence method, which was introduced in [M. Akhmetov, Asymptotic representation of solutions of regularly perturbed systems of differential equations with a nonclassical right-hand side, Ukrainian Math. J. 43 (1991) 1209-1214; M. Akhmetov, On the expansion of solutions to differential equations with discontinuou...
Bifurcation of discontinuous limit cycles of the Van der Pol equation Akhmet, Marat (2014-01-01) In this paper, we apply the methods of B-equivalence and psi-substitution to prove the existence of discontinuous limit cycle for the Van der Pol equation with impacts on surfaces. The result is extended through the center manifold theory for coupled oscillators. The main novelty of the result is that the surfaces, where the jumps occur, are not flat. Examples and simulations are provided to demonstrate the theoretical results as well as application opportunities. (C) 2013 IMACS. Published by Elsevier B.V. ...
Oscillation of fourth-order nonlinear neutral delay dynamic equations Grace, S. R.; Zafer, Ağacık (2015-04-01) In this work we establish some new sufficient conditions for oscillation of fourth-order nonlinear neutral delay dynamic equations of the form (a(t)([x(t) - p(t) x(h(t))](Delta Delta Delta))(alpha))(Delta) + q(t)x(beta)(g(t)) = 0, t is an element of [t(0),infinity) T, where alpha and beta are quotients of positive odd integers with beta <= alpha.
A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms Yücel, Hamdullah; BENNER, Peter (2015-11-01) In this paper, we study the numerical solution of optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms, arising from chemical processes. The symmetric interior penalty Galerkin (SIPG) method with upwinding for the convection term is used as a discretization method. We use a residual-based error estimator for the state and the adjoint variables. An adaptive mesh refinement indicated by a posteriori error estimates is applied. The arising saddle point system...

Citation Formats

M. Akhmet and M. Turan, “Bifurcation in a 3D Hybrid system,” Communications in Applied Analysis, vol. 14, no. 3-4, pp. 311–324, 2010, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79551613544&origin=inward.