On the stability of some systems of exponential difference equations

Abstract

Abstract. In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.

Stability and flip bifurcation of a three‐dimensional exponential system of difference equations

“…Natural generalizations of cyclic systems are the, so‐called, close‐to‐cyclic systems of difference equations (see, e.g., previous studies 4‐8 ). Close‐to‐cyclic systems are also natural generalizations of close‐to‐symmetric ones, which have attracted some considerable attention recently (see, e.g., other studies 9‐34 ).…”

“…An interesting dynamical behavior is featured in difference equations systems whose the characteristic polynomial of their linearization has zeros belonging on the unit circle (e.g., other studies 4,5,20,35‐38 ), a case for which Carr 39 and Kuznetsov 40 gave some classical results. A basic biological model of this category can be found in Berg and Stević 10 and in Stević, 38 where the method of the last paper can be modified and applied to some other equations and systems, as for example, was conducted in previous studies 24,29‐34,41‐44 .…”

Global Dynamics of Higher-Order Exponential Systems of Difference Equations

“…where , , , 1 , 1 , 1 and , ( = 0, −1) are positive real numbers. Psarros et al [8] have explored the dynamical properties of the following six exponential systems of difference equations:…”

Multiple solutions of fourth-order difference equations with different boundary conditions

“…Recently, some literature [11,12] studied solutions of φ c -Laplacian difference equations. For more research on solutions of difference equations, we can refer to [13][14][15][16][17][18][19][20][21][28][29][30][31].…”