Papers by Mustafa Kulenović
DergiPark (Istanbul University), Apr 1, 2019
We investigate the global asymptotic stability of the difference equation of the form with positi... more We investigate the global asymptotic stability of the difference equation of the form with positive parameters and nonnegative initial conditions such that x0 + x-1 > 0 . The map associated to this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the parametric space. In some cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability.
The Scientific World Journal, 2014
By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mir... more By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation:xn+1=(2axn)/(1+xn2)-xn-1, n=0,1,…, wherex-1,x0∈(-∞,∞), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions.
Nonlinear Analysis: Theory, Methods & Applications, 2003
Consider the system of neutral delay di erential equations where p ∈ R; ∈ (0; ∞); ∈ [0; ∞] and Q ... more Consider the system of neutral delay di erential equations where p ∈ R; ∈ (0; ∞); ∈ [0; ∞] and Q is continuous matrix, and the system d dt (x(t) + Bx(t - where B is a matrix. We obtain the su cient condition for the existence of certain types of solutions of the above equation to be ∞ Q(s) ds ¡ ∞ for p = -1.
Journal of Mathematical Analysis and Applications, 2005
We investigate the global asymptotic behavior of solutions of the system of difference equations ... more We investigate the global asymptotic behavior of solutions of the system of difference equations where the parameters a, b, c, d, e, and f are in (0, ∞) and the initial conditions x 0 , y 0 , and z 0 are arbitrary non-negative numbers. We obtain some global attractivity results for the positive equilibrium of this system for different values of the parameters.
Journal of Inequalities and Applications, 2005
We investigate the global asymptotic behavior of solutions of the system of difference equations ... more We investigate the global asymptotic behavior of solutions of the system of difference equations x n+1 = (a + x n )/(b + y n ), y n+1 = (d + y n )/(e + x n ), n = 0,1,..., where the parameters a, b, d, and e are positive numbers and the initial conditions x 0 and y 0 are arbitrary nonnegative numbers. We obtain some asymptotic results for the positive equilibrium of this system.
Journal of Difference Equations and Applications, 2005
We investigate the global character of solutions of the system of difference equationswith positi... more We investigate the global character of solutions of the system of difference equationswith positive parameters and non-negative initial conditions.
Discrete Dynamics in Nature and Society, 2013
Consider the difference equationxn+1=f(xn,…,xn−k),n=0,1,…,wherek∈{1,2,…}and the initial condition... more Consider the difference equationxn+1=f(xn,…,xn−k),n=0,1,…,wherek∈{1,2,…}and the initial conditions are real numbers. We investigate the existence and nonexistence of the minimal period-two solution of this equation when it can be rewritten as the nonautonomous linear equationxn+l=∑i=1−lkgixn−i,n=0,1,…,wherel,k∈{1,2,…}and the functionsgi:ℝk+l→ℝ. We give some necessary and sufficient conditions for the equation to have a minimal period-two solution whenl=1.
Advances in Difference Equations, 2007
We investigate the global stability character of the equilibrium points and the period-two soluti... more We investigate the global stability character of the equilibrium points and the period-two solutions of y n+1 = (py n + y n-1 )/(r + qy n + y n-1 ), n = 0,1,..., with positive parameters and nonnegative initial conditions. We show that every solution of the equation in the title converges to either the zero equilibrium, the positive equilibrium, or the period-two solution, for all values of parameters outside of a specific set defined in the paper. In the case when the equilibrium points and period-two solution coexist, we give a precise description of the basins of attraction of all points. Our results give an affirmative answer to Conjecture 9.5.6 and the complete answer to Open Problem 9.5.7 of
Advances in Difference Equations, 2006
We investigate the global asymptotic behavior of solutions of the system of difference equations ... more We investigate the global asymptotic behavior of solutions of the system of difference equations x n+1 = (a + x n )/(b + y n ), y n+1 = (d + y n )/(e + x n ), n = 0,1,..., where the parameters a,b,d, and e are positive numbers and the initial conditions x 0 and y 0 are arbitrary nonnegative numbers. In certain range of parameters, we prove the existence of the global stable manifold of the unique positive equilibrium of this system which is the graph of an increasing curve. We show that the stable manifold of this system separates the positive quadrant of initial conditions into basins of attraction of two types of asymptotic behavior. In the case where a = d and b = e, we find an explicit equation for the stable manifold to be y = x.
Journal of Mathematical Analysis and Applications, 2005
We investigate the stability of solutions of the Gumowski-Mira equation with a period-two coeffic... more We investigate the stability of solutions of the Gumowski-Mira equation with a period-two coefficient: and the initial values y -1 , y 0 are real numbers.
Dynamics of Second Order Rational Difference Equations, 2001
Discrete Dynamical Systems and Difference Equations with Mathematica, 2002
W AII I . A 11 «JT / s \ DISCRETE DYNAMICAL SYSTEMS DiFFERENCE EQUATIONS with Mathematics Hsiifti... more W AII I . A 11 «JT / s \ DISCRETE DYNAMICAL SYSTEMS DiFFERENCE EQUATIONS with Mathematics HsiiftiisaS Orlando Merino ^f CHAPMAN & HALLCRC ... DISCRETE DYNAMICAL SYSTEMS and DIFFERENCE EQUATIONS with Mathematica This O 354U-7S6-0GY7
Nonlinear Analysis: Theory, Methods & Applications, 2001
Journal of Dynamics and Differential Equations, 1990
ABSTRACT
Journal of Difference Equations and Applications, 2006
... DOI: 10.1080/10236190500410109 MRS Kulenović a * & Orlando Merino a pages 101-108. Av... more ... DOI: 10.1080/10236190500410109 MRS Kulenović a * & Orlando Merino a pages 101-108. Available online: 20 Aug 2006. ...
Journal of Difference Equations and Applications, 2007
We study global attractivity of the period-two coefficient version of the delay logistic differen... more We study global attractivity of the period-two coefficient version of the delay logistic difference equation, also known as Pielou's equation,whereWe prove that for , zero is the unique equilibrium point. If , then zero is globally asymptotically stable, with basin of attraction given by the nonnegative quadrant of initial conditions. If , then zero is unstable, and a sequence converges
Journal of Difference Equations and Applications, 2009
... Merino b pages 303-323. ... On second-order rational difference equations, part 1. J. Differ.... more ... Merino b pages 303-323. ... On second-order rational difference equations, part 1. J. Differ. Equ. Appl. , 13: 9691004. [Taylor & Francis Online], [Web of Science ®] View all references, 22. Ladas, G. 2008a. On second-order rational difference equations, part 2. J. Differ. Equ. Appl. ...
Journal of Difference Equations and Applications, 2002
ABSTRACT We show that the equation in the title with nonnegative parameters and nonnegative initi... more ABSTRACT We show that the equation in the title with nonnegative parameters and nonnegative initial conditions exhibits a trichotomy character concerning periodicity, convergence, and boundedness which depends on whether the parameter n is equal, less, or greater than the sum of the parameters g and A .
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Papers by Mustafa Kulenović