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We investigate the boundedness character of non-negative solutions of a rational system in the plane. The system contains 10 parameters with non-negative real values and consists of 343 special cases, each with positive parameters. In 342 out of the 343 special cases, we establish easily verifiable necessary and sufficient conditions, explicitly stated in terms of 10 parameters, which determine the boundedness character of solutions of the system. In the remaining special case, we conjecture the boundedness character of solutions. It is interesting to note that this special case can be transformed to the well-known May's Host-Parasitoid model. [ABSTRACT FROM AUTHOR]

Edited by Gerry LadasIn this section, we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas. Email: gladas@math.uri.edu [ABSTRACT FROM AUTHOR]

The article presents the first part of a paper about second-order rational difference equations. This study aims to demonstrate the results of the global character of solutions of a second-order rational difference equation. Moreover, a number of open problems and conjectures related to the topic will also be presented in the article.

The article presents several open problems and conjectures on the boundedness character of solutions of some special cases of the kth-order rational difference equation with nonnegative parameters and with arbitrary nonnegative initial conditions. To establish the fact that every solution of the equation is bounded in a large number of special cases, two theorems were presented.

We study a second-order difference equation of the form zn+1=znF(zn-1)+h, where both F(z) and zF(z) are decreasing. We consider a set of invariant curves at h=1 and use it to characterize the behaviour of solutions when h>1 and when 01 is related to the Y2K problem. For 0