VERTICAL AND HORIZONTAL GRAZING

Date

2017-03-01

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

103
views

0
downloads

Grazing solutions of non-autonomous system with variable moments of impulses are examined. Appropriate definitions for vertical and horizontal grazing in non-autonomous systems are given and interpreted geometrically. The linearization for the periodic solutions which have vertical or horizontal grazing is obtained. Examples are presented to demonstrate the practicality of our results and they are visualized by the simulations.

URI

https://hdl.handle.net/11511/54151

Journal

DYNAMIC SYSTEMS AND APPLICATIONS

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Direct numerical simulation of pipe flow using a solenoidal spectral method Tugluk, Ozan; Tarman, Işık Hakan (2012-05-01) In this study, a numerical method based on solenoidal basis functions, for the simulation of incompressible flow through a circular-cylindrical pipe, is presented. The solenoidal bases utilized in the study are formulated using the Legendre polynomials. Legendre polynomials are favorable, both for the form of the basis functions and for the inner product integrals arising from the Galerkin-type projection used. The projection is performed onto the dual solenoidal bases, eliminating the pressure variable, si...
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 ...
Forced Oscillation of Second-Order Impulsive Differential Equations with Mixed Nonlinearities ÖZBEKLER, ABDULLAH; Zafer, Ağacık (2011-07-08) In this paper we give new oscillation criteria for a class of second-order mixed nonlinear impulsive differential equations having fixed moments of impulse actions. The method is based on the existence of a nonprincipal solution of a related second-order linear homogeneous equation.
Boundary value problems for higher order linear impulsive differential equations Uğur, Ömür; Akhmet, Marat (2006-07-01) In this paper higher order linear impulsive differential equations with fixed moments of impulses subject to linear boundary conditions are studied. Green's formula is defined for piecewise differentiable functions. Properties of Green's functions for higher order impulsive boundary value problems are introduced. An appropriate example of the Green's function for a boundary value problem is provided. Furthermore, eigenvalue problems and basic properties of eigensolutions are considered. (c) 2006 Elsevier In...
Exponential stability of periodic solutions of recurrent neural networks with functional dependence on piecewise constant argument Akhmet, Marat; Cengiz, Nur (The Scientific and Technological Research Council of Turkey, 2018-01-01) In this study, we develop a model of recurrent neural networks with functional dependence on piecewise constant argument of generalized type. Using the theoretical results obtained for functional differential equations with piecewise constant argument, we investigate conditions for existence and uniqueness of solutions, bounded solutions, and exponential stability of periodic solutions. We provide conditions based on the parameters of the model.

Citation Formats

M. Akhmet, “VERTICAL AND HORIZONTAL GRAZING,” DYNAMIC SYSTEMS AND APPLICATIONS, pp. 131–145, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54151.