# Mehmed NurkanovićUniversity of Tuzla | UNTZ · Department of Mathematics

Mehmed Nurkanović

Professor

## About

73

Publications

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583

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Introduction

Additional affiliations

April 1990 - present

## Publications

Publications (73)

This paper investigates the dynamics of non-autonomous cooperative systems of difference equations with asymptotically constant coefficients. We are mainly interested in global attractivity results for such systems and the application of such results to evolutionary population cooperation models. We use two methods to extend the global attractivity...

This paper investigates the rate of convergence of a certain mixed monotone rational second-order difference equation with quadratic terms. More precisely we give the precise rate of convergence for all attractors of the difference equation $x_{n+1}=\frac{Ax_{n}^{2}+Ex_{n-1}}{x_{n}^{2}+f}$, where all parameters are positive and initial conditions a...

This paper investigates an autonomous discrete-time glycolytic oscillator model with a unique positive equilibrium point which exhibits chaos in the sense of Li–Yorke in a certain region of the parameters. We use Marotto’s theorem to prove the existence of chaos by finding a snap-back repeller. The illustration of the results is presented by using...

We use the Kolmogorov-Arnold-Moser (KAM) theory to investigate the stability of solutions of a system of difference equations, a certain class of a generalized May's host-parasitoid model. We show the existence of the extinction, interior, and boundary equilibrium points and examine their stability. When the rate of increase of hosts is less than o...

In teaching mathematics to first-year undergraduates, and thus in the appropriate calculus textbooks, the task of calculating an integral that satisfies a specific first-order or second-order recurrence relation often appears. These relations are obtained mainly by applying the method of integration by parts. Calculating such integrals is usually t...

This paper investigates the dynamics of non-autonomous competitive systems of difference equations with asymptotically constant coefficients. We are mainly interested in global attractivity results for such systems and the application of such results to the evolutionary population of competition models of two species.

It is cover page of new issue of "Sarajevo Journal of Mathemetics" prepared by two Editors in Chief: Academician Mirjana Vuković, ANUBiH and Prof. Mehmed Nurkanović, University of Tuzla

This paper investigates an autonomous predator-prey system of difference equations with three equilibrium points and exhibits chaos in the sense of Li-Yorke in the positive equilibrium point. Numerical simulations are presented to illustrate our results.

This paper investigates the local and global character of the unique positive equilibrium of certain mixed monotone rational second-order difference equation with quadratic terms. The equation’s corresponding associated map is always decreasing for the second variable and can be either decreasing or increasing for the first variable depending on th...

We use the epidemic threshold parameter, \({{\mathcal {R}}}_{0}\), and invariant rectangles to investigate the global asymptotic behavior of solutions of the density-dependent discrete-time SI epidemic model where the variables \(S_{n}\) and \(I_{n}\) represent the populations of susceptibles and infectives at time \(n = 0,1,\ldots \), respectively...

In this chapter, by using the Kolmogorov-Arnold-Moser (KAM) theory, we investigate the stability of the positive elliptic equilibrium point of the difference equation
x_{n+1}=((Ax_{n}³+B)/(ax_{n-1})), n=0,1,2,…
where the parameters A,B,a and the initial conditions x₋₁,x₀ are positive numbers. The specific feature of this difference equation is th...

This book covers key areas of mathematics and computer science. The contributions by the authors include electrostatic effect, Gibbs energy principal, equilibrium theory, Lyapunov function, Global stability, area preserving map, Birkho normal form, KAM theorem, synthetic tableaux, principle of bivalence, cut; first-order theory, universal axiom, co...

We investigate the local and global character of the unique equilibrium point and boundedness of the solutions of certain homogeneous fractional difference equation with quadratic terms. Also, we consider Neimark–Sacker bifurcations and give the asymptotic approximation of the invariant curve.
1. Introduction and Preliminaries
In this paper, the s...

Dedicated to the memory of Accademicians Harry I. Miller and Fikret Vajzović, our teachers and supporters. ABSTRACT. We investigate the global dynamics of the following rational difference equation of second order x n+1 = Ax 2 n + Ex n−1 x 2 n + f , n = 0, 1,. .. , where the parameters A and E are positive real numbers and the initial conditions x...

We investigate the local and global character of the unique equilibrium point
of certain homogeneous fractional difference equation with quadratic terms. The
existence of the period-two solution in one special case is given. Also, in this case
the local and global stability of the minimal period-two solution for some special
values of the parameter...

We investigate the global asymptotic stability of the following second order rational difference equation of the form xn+1=Bxnxn-1+F/bxnxn-1+cxn-12, n=0,1,…, where the parameters B , F , b , and c and initial conditions x-1 and x0 are positive real numbers. The map associated with this equation is always decreasing in the second variable and can be...

We investigate global dynamics of the following second order rational difference equation x n+1 = x n x n−1 +αx n +βx n−1 ax n x n−1 +bx n−1 , where the parameters α, β, a, b are positive real numbers and initial conditions x −1 and x 0 are arbitrary positive real numbers. The map associated to the right-hand side of this equation is always decreas...

We investigate the local and global character of the unique equilibrium point,
the existence and the local stability of the period-two solutions of certain homogeneous fractional difference equation with quadratic terms. The local stability and
global attractivity results of the minimal period-two solution in one special case are
given. Also, we in...

By using the Kolmogorov-Arnold-Moser (KAM) theory, we investigate the stability of the positive elliptic equilibrium point of the difference equation xn+1 = Ax 3 n + B axn−1 , n = 0, 1, 2,. .. where the parameters A, B, a and the initial conditions x−1, x0 are positive numbers. The specific feature of this difference equation is the fact that we we...

By using the Kolmogorov–Arnold–Moser theory, we investigate the stability of the equilibrium solution of the difference equation
where A,B,D > 0,u−1,u0>0. We also use the symmetries to find effectively the periodic solutions with feasible periods. Copyright © 2016 John Wiley & Sons, Ltd.

We present a complete local dynamics and investigate the global dynamics of the following second-order difference equation: x(n+1) = (Ax(n)(2) + Ex(n-1) + F)/(ax(n)(2) +ex(n-1) = f), n = 0, 1, 2..., where the parameters A, E, F, a, e, and f are nonnegative numbers with condition A + E + F > 0, a + e + f > 0, and the initial conditions x(-1), x(0) a...

We investigate global dynamics of the equation
x_{n+1}=((x_{n-1})/(ax_{n}²+ex_{n-1}+f)), n=0,1,2,...,
where the parameters a,e and f are nonnegative numbers with condition a+e+f>0 and the initial conditions x₋₁,x₀ are arbritary nonnegative numbers such that x₋₁+x₀>0. The global dynamics of this equation is the result of three bifurcations, two ex...

We investigate the local and global dynamics of the following difference equation
x_{n+1}=((Ax_{n}²+Ex_{n-1}+F)/(ax_{n}²+ex_{n-1}+f)), n=0,1,2,...
where the parameters A,E,F,a,e,f are nonnegative numbers with condition A+E+F>0, a+e+f>0 and the initial conditions x₋₁,x₀ are arbitrary nonnegative numbers such that ax_{n}²+ex_{n-1}+f>0,n=0,1,2,....

We investigate the basins of attraction of equilibrium points and period-two solution of the difference equation of the form x n+1 = Bx n x n−1 + Cx 2 n−1 ax 2 n + bx n x n−1 , n = 0, 1,. .. , where the parameters a, b, C, B are positive numbers and the initial conditions x −1 , x 0 are arbitrary nonnegative numbers. We show that this equation exhi...

We investigate the basins of attraction of equilibrium points and period-two solution of the difference equation of the form x n+1 = Bx n x n−1 + Cx 2 n−1 ax 2 n + bx n x n−1 , n = 0, 1,. .. , where the parameters a, b, C, B are positive numbers and the initial conditions x −1 , x 0 are arbitrary nonnegative numbers. We show that this equation exhi...

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x(n+1) = x(n-1)(2)/(ax(n)(2) + bx(n)x(n-1) + cx(n-1)(2)), n = 0, 1, 2,..., where the parameters a, b, and c are positive numbers and the initial conditions x(-1) and x(0) are arbitrary nonnegative numbers. The unique...

We investigate the basins of attraction of equilibrium points and period-two solutions of the difference equation of the form x(n+1) = f (x(n), x(n-1)), n = 0. 1, ... , where f is decreasing in the first and increasing in the second variable. We show that the boundaries of the basins of attraction of different locally asymptotically stable equilibr...

We investigate the global asymptotic behavior of solutions of the following anti-competitive system of difference equations xn+1 = γ1yn A1 + xn , yn+1 = β2xn + γ2yn yn , n = 0, 1,. .. , where the parameters γ1, γ2, β2, A1 are positive numbers and the initial conditions x0 ≥ 0, y0 > 0. We find the basins of attraction of all at-tractors of the syste...

We investigate the global dynamics of solutions of competitive rational systems of difference equations in the plane. We show that the basins of attractions of different locally asymptotically stable equilibrium points are separated by the global stable manifolds of either saddle points or of non-hyperbolic equilibrium points.

We investigate the global asymptotic behavior of solutions of the following anti-competitive system of rational difference equations x n+1 =γ 1 y n A 1 +x n ,y n+1 =β 2 x n A 2 +y n ,n=0,1,⋯, where the parameters γ 1 ,β 2 ,A 1 and A 2 are positive numbers and the initial conditions x 0 ,y 0 are arbitrary nonnegative numbers. We find the basins of a...

The competitive system of difference equationswhere parameters a, b, d, e are positive real numbers, and the initial conditions and are non-negative real numbers is considered. A complete classification of all possible dynamical behaviour scenarios according to all different parameter configurations is obtained.

We investigate the global asymptotic behavior of solutions of the following anti-competitive system of rational difference equations xn+1 = γ1yn A1 + xn + h, yn+1 = β2xn A2 + yn , n = 0, 1,. .. , where the parameters γ1, β2, A1, A2 and h are positive numbers and the initial conditions x0, y0 are arbitrary nonnegative numbers.

We investigate the global dynamics of solutions of four distinct competitive rational
systems of difference equations in the plane. We show that the basins of attractions of
different locally asymptotically stable equilibrium points are separated by the global stable
manifolds of either saddle points or nonhyperbolic equilibrium points. Our results...

We investigate the global dynamics of solutions of two distinct competitive rational systems of difference equations in the plane. We show that the basins of attraction of different locally asymptotically stable equilibrium points are separated by the global stable manifolds of either saddle points or of non-hyperbolic equilibrium points. Our resul...

We investigate the global stability properties and asymptotic behavior of solutions of the system of difference equations Xn+1 = Xn/a+Yn2, Yn+1 = Yn/b+Xn2, n = 0, 1,... where the parameters a and b are positive numbers, and the initial conditions x0 and y0 are arbitrary nonnegative numbers.

In a modelling setting, the rational system of nonnlinear difference equations 1 1 2 2 , , 0 , 1 , n n n n n n x y x y n a y b x + + = = = + + K represents the rule by which two discrete, competitive populations reproduce from one generation to the next. The phase variables n x and n y denote population sizes during the n-th generation and sequence...

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 glo...

We investigate the global asymptotic behavior of solutions of the system of difference equations xn+1 = (a + xn)/(b + y n), yn+1 = (d + yn)/(e + xn), n = 0, 1,..., where the parameters a, b, d, and e are positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. We obtain some asymptotic results for the positive equili...

Dedicated to Allan Peterson on the Occasion of His 60th Birthday.We investigate the global asymptotic behavior of solutions of the system of difference equations where the parameters A and B are in (0, ∞) and the initial conditions x0 and y0 are arbitrary nonnegative numbers. We show that the stable manifold of this system separates the positive qu...

We investigate the global dynamics of solutions of two distinct competitive rational systems of difference equations in the plane. We show that the basins of attraction of different locally asymptotically stable equilibrium points are separated by the global stable manifolds of either saddle points or of non-hyperbolic equilibrium points. Our resul...