Invariants for Difference Equations and Systems of Difference Equations of Rational Form

Abstract

We present some invariants for difference equations and systems of difference equations of rational form. We examine two cases. In the first case the coefficients are constant and in the second are positive periodic sequences of certain periods.ᮊ 1997 Academic Press

Solvability and semi‐cycle analysis of a class of nonlinear systems of difference equations

“…for n ∈ N 0 (in fact, (45) holds also for n = −1). From (23), (27) and (45), it follows that the general solution to system (41) is given by…”

“…Hence, we have that formula (45) holds. By using (45) in the relation n = √ a e (v n ), n ≥ − 1, (24) with n = −2, − 1, and the following equality v −1 = ln…”

“…34,36 On the other hand, Papaschinopoulos and Schinas started studying symmetric and related systems two decades ago. [37][38][39][40][41][42][43][44][45][46] Regarding solvability methods, they were usually more interested in invariants, [38][39][40]44,45,47 although they have also some results on finding closed-form formulas such as in Papaschinopoulos and Stefanidou. 28 This motivated us to study also some systems of difference equations (see, eg, previous studies 25,26,[31][32][33][34][35][48][49][50][51][52] ).…”

Solution for Rational Systems of Difference Equations of Order Three

“…Schinas [10] studied some invariants for difference equations and systems of difference equations of rational form.…”

On the nonlinear difference equation system xn+1=A+yn−m/Yu1, Yang2, Evans3 et al. 2007Computers & Mathematics with Applications22000View full textAdd to dashboardCite

“…In recent years, nonlinear difference equation systems have attracted considerable interest [2][3][4][5][6][7][8]. In particular, Papaschinopoulos and Papadopoulos [5] studied the dynamics of positive solutions to the system of rational difference equations…”