On the behaviour of the solutions of a $k$-order cyclic-type system of max difference equations

Abstract

summary:We investigate the behaviour of the solutions of a $k$-dimensional cyclic system of difference equations with maximum. More precisely, we study the existence and the number of the equilibria in the case when $k$ is an odd or an even positive integer, but also for the various values of the exponents of the terms of the difference equations of this system. In addition, we find invariant intervals for our system and we invistegate the convergence of the solutions to the unique positive equilibrium. Finally, we study the asymptotic behavior of the positive solutions of the system in the case, where $k=2$ and $k=4$