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On a class of difference equations withinterlacing indices
(Springer, 2021-06-16)Some results on the long-term behavior of solutions to a class of difference equations,which includes numerous nonlinear difference equations of various orders thatattracted some attention in the last 15 years, are presented. ... -
Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators
(MDPI, 2021-02-05)The main objective of our paper is to focus on the study of sequences (finite or countable) of groups and hypergroups of linear differential operators of decreasing orders. By using a suitable ordering or preordering of ... -
Note on some representations of general solutions to homogeneous linear difference equations
(Springer Nature, 2020-09-10)It is known that every solution to the second-order difference equation x(n) = x(n-1) + x(n-2) = 0, n >= 2, can be written in the following form x(n) = x(0)f(n-1) + x(1)f(n), where fn is the Fibonacci sequence. Here we ... -
Solvability of a class of hyperbolic-cosine-type difference equations
(Springer Nature, 2020-10-07)We describe a method for constructing one of the basic classes of solvable hyperbolic-cosine-type difference equations, generalizing a known difference equation by Laplace in a natural way. -
Stabilization of cycles for difference equations with a noisy PF control
(Elsevier, 2020-02-21)Difference equations, such as a Ricker map, for an increased value of the parameter, experience instability of the positive equilibrium and transition to deterministic chaos. To achieve stabilization, various methods can ... -
Boundedness character of a fourth-order system of difference equations
(Springer Nature, 2015-12-01)Sufficient conditions for boundedness character of solutions of a fourth-order system of difference equations is given. -
Existence of solutions converging to zero for nonlinear delayed differential systems
(Springer, 2015-11-17)Je prezentován výsledek o asymptotickém chování dvourozměrného systému diferenciálních rovnic se zpožděním splňujícího jisté postačující podmínky. Jsou zobecněny předcházející výsledky, které byly dokázány užitím ... -
Exponential Stability of Linear Discrete Systems with Multiple Delays
(Hindawi, 2018-08-01)The paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay $x\left( {k+1} \right)=Ax\left( k \right)+\sum_{i=1}^sB_ix\left( ... -
On a product-type system of difference equations of second order solvable in closed form
(BioMed Central, 2015-10-12)Sufficient conditions for solving a system of difference equations of second order in closed form are given. Moreover, sufficient conditions for existence of periodic solutions and asymptotic stability of solutions are ... -
Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R^2
(Hindawi, 2017-06-12)Two-dimensional linear discrete systems $$ x(k+1)=Ax(k)+\sum\limits_{l=1}^{n}B_{l}x_{l}(k-m_{l}),\,\,\,k\ge 0 $$are analyzed, where $m_{1}, m_{2},\dots, m_{n}$ are constant integer delays, $0<m_{1}<m_{2}<\dots<m_{n}$, $A$, ... -
Exponential stability of perturbed linear discrete systems
(Springer, 2016-01-29)V člá nku je studována exponenciální stabilita a konvergence řešení homogenní perturbované soustavy lineárních diskrétních systémů. Nová kritéria exponenciální stability jsou odvozena pomocí druhé metody Ljapunova. Jsou ... -
Lower and upper estimates of solutions to systems of delay dynamic equations on time scales
(Springer, 2013-11-27)In this paper we study a system of delay dynamic equations on the time scale $\T$ of the form $$y^{\Delta}(t)=f(t,y_{\tau}(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$, $y_\tau(t)=(y_1(\tau_ ... -
Modelling precipitation extremes in the Czech Republic: Update of intensity-duration-frequency curves
(Estonian Academy Publishers, 2016-12-20)Precipitation records from six stations of the Czech Hydrometeorological Institute were subject to statistical analysis with the objectives of updating the Intensity-Duration-Frequency (IDF) curves, by applying extreme ... -
The Symmetry of Lower and Upper Approximation, Determined by a Cyclic Hypergroup, Applicable in Control Theory
(MDPI, 2020-01-03)In the first part of our paper, we construct a cyclic hypergroup of matrices using the Ends Lemma. Its properties are then, in the second part of the paper, used to describe the symmetry of lower and upper approximations ... -
New families of third-order iterative methods for finding multiple roots
(Hindawi, 2014-06-15)Two families of third-order iterative methods for finding multiple roots of nonlinear equations are developed in this paper. Mild conditions are given to assure the cubic convergence of two iteration schemes (I) and (II). ... -
Semilocal Convergence Theorem for the Inverse-Free Jarratt Method under New Hölder Conditions
(Hindawi, 2015-02-05)Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence ... -
A novel iterative scheme and its application to differential equations
(Hindawi, 2014-02-20)The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian ... -
Newton-Kantorovich and Smale uniform type convergence theorem for a deformed Newton method in Banach spaces
(Hindawi, 2013-12-02)Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is ... -
General explicit solution of planar weakly delayed linear discrete systems and pasting its solutions
(Hindawi, 2014-04-29)Planar linear discrete systems with constant coefficients and delays are considered. It is assumed that the considered system is weakly delayed. The characteristic equations of such systems are identical with those for the ... -
Representation of the solutions of linear discrete systems with constant coefficients and two delays
(Hindawi, 2014-05-13)Cílem článku je vytvořit metodu konstrukce řešení počátečních úloh pro lineární diskrétní systémy s konstantními koeficienty a dvěma zpožděními. Řešení jsou vyjádřena pomocí speciální funkce zvané diskrétní zpožděná maticová ...
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