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  1. 17 Fasciculi Mathematici
  2. 11 Demonstratio Mathematica
  3. 4 Acta Mechanica et Automatica
  4. 2 Annales Polonici Mathematici
  5. 2 International Journal of Applied Mathematics and Computer Science
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  1. 2 2023
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  2. 2 Bolat Y.
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  4. 2 Elsayed E. M.
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1
Content available remote Oscillation of difference equations with several positive and negative coefficients
100%
Öğünmez H. , Öcalan Ö.
Fasciculi Mathematici
|
2013
|
tom Nr 51
115--122
EN
Our aim in this paper is to obtain sufficient conditions for the oscillation of every solution of first order difference equations ...[wzór] where pi, qi ∈ R+ and ki, li ∈ N for i = 1, 2,..., m.
2
Content available remote On the behaviour of rational first order difference equation with constant coefficients
80%
Magnucka-Blandzi E. , Popenda J.
|
1998
|
tom Vol. 31, nr 2
405-416
3
Content available remote On the solution of recursive sequence of order two
80%
Elsayed E. M.
Fasciculi Mathematici
|
2008
|
tom Nr 40
5-13
EN
We obtain in this paper the solution of the following difference equation (formula), n= 0, 1,... where the initial conditions x-1, x0 are arbitrary real numbers.
4
Content available Analysis and Applications of Composed Forms of Caputo Fractional Derivatives
80%
Błaszczyk T. , Kotela E. , Hall M. R. , Leszczyński J.
Acta Mechanica et Automatica
|
2011
|
tom Vol. 5, no. 2
11-14
EN
In this paper we consider two ordinary fractional differential equations with composition of the left and the right Caputo derivatives. Analytical solution of this type of equations is known for particular cases, having a complex form, and therefore is difficult in practical calculations. Here, we present two numerical schemes being dependent on a fractional order of equation. The results of numerical calculations are compared with analytical solutions and then we illustrate convergence of our schemes. Finally, we show an application of the considered equation.
5
Content available Variable-, Fractional-Orders Closed-Loop Systems Description
80%
Ostalczyk P.
Acta Mechanica et Automatica
|
2011
|
tom Vol. 5, no. 2
79-85
EN
In this paper we explore the linear difference equations with fractional orders, which are functions of time. A description of closed-loop dynamical systems described by such equations is proposed. In a numerical example a simple control strategy based on time-varying fractional orders is presented.
6
Content available Investigation of Fixed-Point Computation Influence on Numerical Solutions of Fractional Differential Equations
80%
Piątek P. , Baranowski J.
Acta Mechanica et Automatica
|
2011
|
tom Vol. 5, no. 2
101-107
EN
In this paper the problem of the influence of fixed point computation on numerical solutions of linear differential equations of fractional order is considered. It is a practically important problem, because of potential possibilities of using dynamical systems of fractional order in the tasks of control and filtering. Discussion includes numerical method is based on the Grünwald-Letnikov fractional derivative and how the application of fixed-point architecture influences its operation. Conclusions are illustrated with results of floating-point arithmetic with double precision and fixed point arithmetic with dif- ferent word lengths.
7
Content available remote Asymptotic behavior of solutions of second order neutral difference equations with "maxima"
80%
Luo J. , Yu Y.
|
2001
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tom Vol. 34, nr 1
83-89
EN
Second order neutral difference equations with "maxima" are considered and some asymptotic properties of nonoscillatory solutions are given.
8
Content available remote On semicycles of solutions of nonlinear difference equations with several delays
80%
Li C. F. , Zhou Y. , Luo X. N.
|
2003
|
tom Vol. 36, nr 1
105--112
9
Content available remote Kamenev-type oscillation criteria for hyperbolic delay difference equations
80%
Kubiaczyk I. , Saker S. H.
|
2003
|
tom Vol. 36, nr 1
113--122
EN
Some new oscillation criteria and discrete Kamenev-type oscillation criteria for hyperbolic nonlinear delay difference equations are obtained.
10
Content available remote Fonctions zêta d'Igusa et fonctions hypergéométriques
80%
Dan N.
|
1999
|
tom 71
|
nr 1
61-86
FR
On étudie la fonction zêta d'Igusa ζ(P,s) associée à une hypersurface projective complexe {P = 0}. On montre qu'elle est une intégrale d'Euler généralisée et on précise le système différentiel A-hypergéométrique qu'elle satisfait. On indique un algorithme pour la détermination explicite d'une équation aux différences satisfaite par ζ(P,s). On calcule explicitement cette fonction pour quelques cas particuliers. On prouve que la fonction zêta associée au résultant $R_{(1,2)}$ n'est pas une somme de produits de fonctions exponentielles et gamma.
11
Content available remote Terminal control problem for processes represented by nonlinear multi parameter binary dynamic system
80%
Haci Y. H. , Ozen K.
Control and Cybernetics
|
2009
|
tom Vol. 38, no 3
625-633
EN
In this paper, nonlinear multi parameter binary difference equation system (MPBDS) and optimal piecewise process are analyzed. Since such difference equation system is over-determined, a theorem similar to Frobenius's theorem is proved on Galois field. An illustrative example, which can be solved by applying terminal control problem is given. Then, terminal control problem is examined and it is shown that the principle of optimality is satisfied.
12
Content available remote Convergence and periodic properties of solutions for a class of delay difference equation
80%
Zhu H. , Huang L.
Fasciculi Mathematici
|
2007
|
tom Nr 37
121-128
EN
We propose a class of delay difference equation with piecewise constant nonlinearity. The convergence of solutions and the existence of globally asymptotically stable periodic solutions are investigated for such a class of difference equation.
13
Content available remote Oscillations of fourth order quasilinear difference equations
80%
Thandapani E. , Selvaraj B.
Fasciculi Mathematici
|
2007
|
tom Nr 37
109-119
EN
Consider the fourth order quasilinear difference equation of the form where {pn} is a positive sequence and {qn} is a sequence of non-negative reals, a and ,3 are ratios of odd positive integers. We obtain some new sufficient conditions for the oscillation of all solutions of equation (*). Examples are inserted to illustrate the importance of our results.
14
Content available remote Further instances of periodicity in May's host parasitoid equation
80%
Sizer W. S.
Fasciculi Mathematici
|
2010
|
tom Nr 44
115-121
EN
May’s host parasitoid equation is the difference equation (1) ...[wzór] We show that for each &slpha; there is a number k such that, whenever n > k, equation (1) has a one cycle periodic solution of period n. We also give some results on two cycle periodic solutions.
15
Content available remote On a class of rational difference equations
80%
Atasever N. , Yalcinkaya I.
Fasciculi Mathematici
|
2010
|
tom Nr 43
13-18
EN
In this paper we study the behavior of the positive solutions of the following nonlinear difference equation ...[wzór], n = 0, 1, 2, ... where the initial values ...[wzór] and k = 0, 1, 2, . . ..
16
Content available Periodic, nonperiodic, and chaotic solutions for a class of difference equations with negative feedback
80%
Kennedy B. B.
Opuscula Mathematica
|
2023
|
tom Vol. 43, no. 4
507--546
EN
We study the scalar difference equation [formula], where f is nonincreasing with negative feedback. This equation is a discretization of the well-studied differential delay equation x′(t) = f(x(t − 1)). We examine explicit families of such equations for which we can find, for infinitely many values of N and appropriate parameter values, various dynamical behaviors including periodic solutions with large numbers of sign changes per minimal period, solutions that do not converge to periodic solutions, and chaos. We contrast these behaviors with the dynamics of the limiting differential equation. Our primary tool is the analysis of return maps for the difference equations that are conjugate to continuous self-maps of the circle.
17
Content available remote Asymptotic dichotomy for nonoscillatory solutions of a nonlinear difference equation
80%
Zhang G. , Cheng S. S.
Applicationes Mathematicae
|
1998-1999
|
tom 25
|
nr 4
393-399
EN
A nonlinear difference equation involving the maximum function is studied. We derive sufficient conditions in order that eventually positive or eventually negative solutions tend to zero or to positive or negative infinity.
18
Content available remote Locally Lipschitz mappings and asymptotic behaviour of solutions of difference equations in Banach spaces
80%
Gonzales C. , Jimenez-Melado A.
|
2001
|
tom Vol. 34, nr 3
635-640
19
Content available remote Meromorphic solutions of linear difference equations with polynomial coefficients
80%
Zhang Y. , Gao Z. , Zhang H.
Fasciculi Mathematici
|
2017
|
tom Nr 59
159--168
EN
We study the growth of the transcendental meromorphic solution f(z) of the linear difference equation: [formula] where q(z), p0(z), . . ., pn(z) (n ≥ 1) are polynomials such that p0(z)pn(z) ≠ 0, and obtain some necessary conditions guaranteeing that the order of ƒ(z) satisfies σ(ƒ) ≥ 1 using a difference analogue of the Wiman-Valiron theory. Moreover, we give the form of ƒ(z) with two Borel exceptional values when two of p0(z), . . ., pn(z) have the maximal degrees.
20
Content available On asymptotic stability of a linear difference equation depending on parameters
80%
Przyłuski M.
Challenges of Modern Technology
|
2012
|
tom Vol. 3, no. 3
11--14
EN
The paper focuses on a linear diffrence equation depending on parameters. The equation is related to Good win’s theory of extrapolative expectations. The stability region of the equation is investigated. Conditions for asymptotic stability are formulated and presented as an optimisation problem, which is further analysed. Despite employing state-of-the-art solvers, numerical results have turned out to be too ambiguous to provide the basis for definite conclusions about the investigated stability region.
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