Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Bifurcation of a non-smooth planar limit cycle from a vertex
Date
2009-12-15
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
82
views
0
downloads
Cite This
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 discontinuous right-hand side in a series in initial data and parameters, Ukrainian Math. J. 45 (1993) 786-789; M. Akhmetov, N.A. Perestyuk, Differential properties of solutions and integral surfaces of nonlinear impulse systems, Differential Equations 28 (1992) 445-453] (see also [E. Akalin, M. U. Akhmet, The principles of B-smooth discontinuous flows, Math. Comput. Simul. 49 (2005) 981-995; M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Anal. 60 (2005) 163-178]), these systems are reduced to impulsive differential equations. Sufficient conditions are established for the existence of foci and centers both in the noncritical and critical cases. Hopf bifurcation is considered from a vertex, which unites several curves, in the critical case. An appropriate example is provided to illustrate the results.
Subject Keywords
Non-smooth planar systems
,
Focus
,
Center
,
Hopf bifurcation
,
Poincare map
URI
https://hdl.handle.net/11511/44748
Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
DOI
https://doi.org/10.1016/j.na.2009.06.031
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments
Dahiya, R. S.; Zafer, A. (Springer Science and Business Media LLC, 2007)
We derive oscillation criteria for general-type neutral differential equations [x(t) +αx(t− τ) +βx(t +τ)](n) = δ b ax(t − s)dsq1(t,s) + δ d c x(t + s)dsq2(t,s) = 0, t ≥ t0, where t0 ≥ 0, δ = ±1, τ > 0, b>a ≥ 0, d>c ≥ 0, α and β are real numbers, the functions q1(t,s) : [t0,∞) × [a,b] → R and q2(t,s):[t0,∞) × [c,d] → R are nondecreasing in s for each fixed t, and τ is periodic and continuous with respect to t for each fixed s. In certain special cases, the results obtained generalize and improve s...
Discrete symmetries and nonlocal reductions
GÜRSES, METİN; Pekcan, Asli; Zheltukhın, Kostyantyn (Elsevier BV, 2020-01-31)
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
The geometry of self-dual two-forms
Bilge, AH; Dereli, T; Kocak, S (1997-09-01)
We show that self-dual two-forms in 2n-dimensional spaces determine a n(2)-n+1-dimensional manifold S-2n and the dimension of the maximal linear subspaces of S-2n is equal To the (Radon-Hurwitz) number of linearly independent vector fields on the sphere S2n-1. We provide a direct proof that for n odd S-2n has only one-dimensional linear submanifolds. We exhibit 2(c)-1-dimensional subspaces in dimensions which are multiples of 2(c), for c=1,2,3. In particular, we demonstrate that the seven-dimensional linear...
Finite action Yang-Mills solutions on the group manifold
Dereli, T; Schray, J; Tucker, RW (IOP Publishing, 1996-08-21)
We demonstrate that the left (and right) invariant Maurer-Cartan forms for any semi-simple Lie group enable solutions of the Yang-Mills equations to be constructed on the group manifold equipped with the natural Cartan-Killing metric. For the unitary unimodular groups the Yang-Mills action integral is finite for such solutions. This is explicitly exhibited for the case of SU(3).
Effect of the Jacobian evalution on direct solutions of the Euler equations
Onur, Ömer; Eyi, Sinan; Department of Aerospace Engineering (2003)
A direct method is developed for solving the 2-D planar/axisymmetric Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes, and the resulting nonlinear system of equations are solved using Newton̕s Method. Both analytical and numerical methods are used for Jacobian calculations. Numerical method has the advantage of keeping the Jacobian consistent with the numerical flux vector without extremely complex or impractical analytical differentiations...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Akhmet, “Bifurcation of a non-smooth planar limit cycle from a vertex,”
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
, pp. 0–0, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44748.