Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
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
Almost periodic solutions of differential equations with piecewise constant argument of generalized type
Download
index.pdf
Date
2008-06-01
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
184
views
56
downloads
Cite This
We consider existence and stability of an almost periodic solution of the following hybrid system dx(t) dt = A(t)x(t) + f(t, x(θβ(t)−p1 ), x(θβ(t)−p2 ), . . . , x(θβ(t)−pm )), (1) where x ∈ R n , t ∈ R, β(t) = i if θi ≤ t < θi+1, i = . . .−2, −1, 0, 1, 2, . . . , is an identification function, θi is a strictly ordered sequence of real numbers, unbounded on the left and on the right, pj , j = 1, 2, . . . , m, are fixed integers, and the linear homogeneous system associated with (1) satisfies exponential dichotomy. The deviations of the argument are not restricted by any sign assumption when existence is considered. The problem of positive (almost periodic) solutions of the logistic equation is discussed as an example. A new technique of investigation of equations with piecewise argument, based on integral representation, is developed.
Subject Keywords
Control and Systems Engineering
,
Analysis
,
Computer Science Applications
URI
https://hdl.handle.net/11511/47331
Journal
NONLINEAR ANALYSIS-HYBRID SYSTEMS
DOI
https://doi.org/10.1016/j.nahs.2006.09.002
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
Periodic solutions of the hybrid system with small parameter
Akhmet, Marat; Ergenc, T. (Elsevier BV, 2008-06-01)
In this paper we investigate the existence and stability of the periodic solutions of a quasilinear differential equation with piecewise constant argument. The continuous and differentiable dependence of the solutions on the parameter and the initial value is considered. A new Gronwall-Bellman type lemma is proved. Appropriate examples are constructed.
Time-constrained temporal logic control of multi-affine systems
Aydın Göl, Ebru (Elsevier BV, 2013-11-01)
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 multi-affine 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 estimating the time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition syste...
Exhaustive study on the commutativity of time-varying systems
KÖKSAL, MUHAMMET (Informa UK Limited, 1988-5)
This paper, which is a survey and a compact reference on the commutativity of time-varying systems, gives the complete set of necessary and sufficient commutativity conditions for systems of any order. Original results are derived on Euler's systems, and explicit commutativity conditions are presented for fourth-order systems, which have not yet appeared in the literature.
EXACTLY SOLVABLE EFFECTIVE MASS D-DIMENSIONAL SCHRODINGER EQUATION FOR PSEUDOHARMONIC AND MODIFIED KRATZER PROBLEMS
IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2009-03-01)
The point canonical transformation (PCT) approach is used to solve the Schrodinger equation for an arbitrary dimension D with a power-law position-dependent effective mass (PDEM) distribution function for the pseudoharmonic and modified Kratzer (Mie-type) diatomic molecular potentials. In mapping the transformed exactly solvable D-dimensional (D >= 2) Schrodinger equation with constant mass into the effective mass equation by using a proper transformation, the exact bound state solutions including the energ...
Cyclic codes and reducible additive equations
Guneri, Cem; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2007-02-01)
We prove a Weil-Serre type bound on the number of solutions of a class of reducible additive equations over finite fields. Using the trace representation of cyclic codes, this enables us to write a general estimate for the weights of cyclic codes. We extend Woffmann's weight bound to a larger classes of cyclic codes. In particular, our result is applicable to any cyclic code over F-p and F-p2, where p is an arbitrary prime. Examples indicate that our bound performs very well against the Bose-Chaudhuri-Hocqu...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Akhmet, “Almost periodic solutions of differential equations with piecewise constant argument of generalized type,”
NONLINEAR ANALYSIS-HYBRID SYSTEMS
, pp. 456–467, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47331.