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

206
views

69
downloads

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

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.