The global asymptotic stability of a system of difference equations

Dynamics of System of Higher Order Difference Equations with Quadratic Terms

“…We also consider this system with the initial values t 2 = 3; t 1 = 4; t 0 = 0:6; z 2 = 2; z 1 = 0:4 and z 0 = 3. Thus the solutions of system (10) oscillate about positive equilibrium point ( t; z) = (1:82; 1:82). Figure 2 verifies our theoretical results.…”

“…Additionally, in [10], Gümüş dealt with the global asymptotic stability and rate of convergence of related system. In [3], Beso et al investigated the boundedness and global asymptotic stability of solutions of following difference equation…”

Global behavior of P-dimensional difference equations system

“…Complement of the work above, in [8], Gümüş studied the global asymptotic stability of positive equilibrium, the rate of convergence of positive solutions and he presented some results about the general behavior of solutions of system (2). Our aim in this paper is to generalize the results concerning equation (1) and system (2) to the system of p nonlinear difference equations…”

“…There has been some recent interest in studying the qualitative analysis of difference equations and system of difference equations. Since the beginning of nineties there has be considerable interest in studying systems of difference equations composed by two or three rational difference equations (see, e.g., [4,5,6,2,8,9,11,10,14,15,17,19,20] and the references therein). However, given the multiplicity of factors involved in any epidemic, it will be important to study systems of difference equations composed by many rational difference equations, which is what we will do in this paper.…”

On a general homogeneous three-dimensional system of difference equations

“…In the literature there are many studies on difference equations defined by homogeneous functions, see for instance [1,2,5,7,11,16]. Noting that also a lot of studies are devoted to various models of difference equations and systems, not necessary defined by homogeneous functions, see for example [4,9,10,12,14,18,19,20,21,22,24,25,26,27,28,29].…”