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
Van der Pol oscillators generated from grazing dynamics
Date
2018-01-01
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
57
views
0
downloads
Cite This
In this paper, we take into account two coupled Van der Pol equations with impacts. The main novelty is that the degenerated system for the model admits an oscillation with zero impact velocity. To prove presence of oscillations, beside the perturbation method, the newly developed linearization for dynamics with grazing has been applied. As different from the theoretical results such as Nordmark mapping and Zero time discontinuity mapping, the grazing is examined through another method of discontinuous dynamics, which diminishes the role of mappingsin the analysis. The rich diversity of changes in the dynamics is observed under regular perturbations, since of the grazing discontinuity. By means of the simulation results, the analytical studies are visualized.
URI
https://hdl.handle.net/11511/37155
Journal
Discontinuity, Nonlinearity, and Complexity
DOI
https://doi.org/10.5890/dnc.2018.09.005
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
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. ...
Nonoscillation and asymptotic behaviour for third order nonlinear differential eruptions
Tiryaki, Aydın; Celebi, AO (Institute of Mathematics, Czech Academy of Sciences, 1998-01-01)
In this paper we consider the equation
Oscillation of integro-dynamic equations on time scales
Grace, Said R.; Graef, John R.; Zafer, Ağacık (2013-04-01)
In this paper, the authors initiate the study of oscillation theory for integro-dynamic equations on time-scales. They present some new sufficient conditions guaranteeing that the oscillatory character of the forcing term is inherited by the solutions.
Non-Markovian diffusion over a parabolic potential barrier: Influence of the friction-memory function
YILMAZ, BÜLENT; Ayik, S.; Abe, Y.; Boilley, D. (American Physical Society (APS), 2008-01-01)
The over-passing probability across an inverted parabolic potential barrier is investigated according to the classical and quantal generalized Langevin equations. It is shown that, in the classical case, the asymptotic value of the over-passing probability is determined by a single dominant root of the "characteristic function," and it is given by a simple expression. The expression for the over-passing probability is quite general, and details of dissipation mechanism and memory effects enter into the expr...
Energy Stable Discontinuous Galerkin Finite Element Method for the Allen-Cahn Equation
Karasözen, Bülent; Sariaydin-Filibelioglu, Ayse; Yücel, Hamdullah (2018-05-01)
In this paper, we investigate numerical solution of Allen-Cahn equation with constant and degenerate mobility, and with polynomial and logarithmic energy functionals. We discretize the model equation by symmetric interior penalty Galerkin (SIPG) method in space, and by average vector field (AVF) method in time. We show that the energy stable AVF method as the time integrator for gradient systems like the Allen-Cahn equation satisfies the energy decreasing property for fully discrete scheme. Numerical result...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Akhmet, “Van der Pol oscillators generated from grazing dynamics,”
Discontinuity, Nonlinearity, and Complexity
, pp. 259–274, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37155.