Solution for systems of difference equations of rational form of order two

Dynamical behaviors of the chaotic Brushless DC motors model

“…is an ellipsoid in R 3 for positive parameters k; v q ; q; v d ; d; r; g; T L : As the V k X ð Þ is a continuous function and C is a bounded closed set, then the function (12) can reach its maximum value max V k X ð Þ X 2C 5L on the surface C defined in (13). Obviously,…”

“…The well-known Lorenz system, R€ ossler system, Chua's circuit system, Chen system, L€ u system, and other chaotic dynamical systems are served as important chaotic models for us to study chaos [1][2][3][4][5][6][7]. Chaotic dynamics has been studied in many fields of science and engineering such as physics, biology, electronic circuits, chemistry, chaotic synchronization, secure communication, and mechanical engineering [8][9][10][11][12][13][14][15][16][17][18].…”

Global dynamics of (1,2)- type systems of difference equations

“…This made the study of qualitative behavior of difference equations an active area of research (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and references cited therein). For instance, Touafek and Elsayed [18,19] investigated the behavior of following systems of difference equations:…”

On the solutions of a higher‐order difference equation in terms of generalized Fibonacci sequences

“…Recently, the problem of finding closed-form solutions of rational difference equations and systems of rational of difference equations have gained considerable interest from many mathematicians. In fact, countless papers have been published previously focusing on the aforementioned topic, see for example [5,6,7,16,20] and [21]. Interestingly, some of the solution forms of these equations are even expressible in terms of well-known integer sequences such as the Fibonacci numbers, Horadam numbers and Padovan numbers (see, e.g., [9,11,12,14,22,24,25,26,27,29,34]).…”

“…In fact, as far as we know, there has no known general method to deal with different classes of difference equations solvable in closed-forms. Nevertheless, numerous studies have recently dealt with finding appropriate techniques in solving closed-form solutions of some systems of difference equations (see, e.g., [2,5,6,7,15,23]). …”