Patterns of boundedness of the rational system x_n+1 = ...[wzór] and y_n+1 = ...[wzór]

• Autorzy: Camouzis E. , Drymonis E. , Ladas G.
• Języki publikacji: EN

Abstrakty

EN

We establish the boundedness character of solutions of the rational system in the title, with the parameters α₁, β₁ positive and the remaining eight parameters nonnegative and with arbitrary nonnegative initial conditions such that the denominators are always positive. We present easily verifiable necessary and sufficient conditions, explicitly stated in terms of the parameters, which determine the boundedness character of the system.

Słowa kluczowe

EN

boundedness; rational equations; patterns of boundedness; rational systems

PL

ograniczoność; równanie wymierne; wzorzec

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2010
• Tom: Nr 44
• Strony: 9--18
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Camouzis E.

autor

Drymonis E.

autor

Ladas G.

• American College of Greece Department of Mathematics 6 Gravias Street, 15342 Aghia Paraskevi, Athens, Greece,

Bibliografia

• [1] Amleh A.M., Camouzis E., Ladas G., On the dynamics of a rational difference equation, Part 1, Int. J. Difference Equ., 3(2008), 1-35.
• [2] Amleh A.M., Camouzis E., Ladas G., On the dynamics of a rational difference equation, Part 2, Int. J. Difference Equ., 3(2008), 195-225.
• [3] Amleh A.M., Camouzis E., Ladas G., Radin M., Patterns of boundedness of a rational system in the plane, J. Difference Equ. Appl., (2010).
• [4] Brett A., Camouzis E., Lynd C., Ladas G., On the boundedness character of a rational system, JNMaS, (2009).
• [5] Camouzis E., Boundedness of solutions of a rational system of difference equations, Proceedings of the 14th International Conference on Difference Equations and Applications held in Instanbul, Turkey, July 21-25, 2008, Ugur-Bahcesehir University Publishing Company, Istanbul, Turkey Difference Equations and Applications, ISBN 978-975-6437-80-3 (2009), 157-164.
• [6] Camouzis E., Drymonis E., Ladas G., On the global character of the system xn+1 = ...[wzór] and yn+1 = ...[wzór], Communications on Applied Nonlinear Analysis, 16(2009), 51-64.
• [7] Camouzis E., Drymonis E., Ladas G., Patterns of boundedness of the rational system xn+1 = ...[wzór] and yn+1 = ...[wzór], (to appear).
• [8] Camouzis E., Gilbert A., Heissan M., Ladas G., On the boundedness character of the system xn+1 = ...[wzór] and yn+1 = ...[wzór], Communications in Mathematical Analysis, (2009).
• [9] Camouzis E., Kulenović M.R.S., Ladas G., Merino O., Rational Systems in the Plane, J. Difference Equ. Appl., 15(2009), 303-323.
• [10] Camouzis E., Ladas G., Dynamics of Third-Order Rational Difference Equations; With Open Problems and Conjectures, Chapman & Hall/CRC Press, 2008.
• [11] Camouzis E., Ladas G., Global results on rational systems in the plane, I, J. Difference. Equ. Appl., (2009).
• [12] Camouzis E., Ladas G., Wu L., On the global character of the system xn+1 = ...[wzór] and yn+1 = ...[wzór], Int. J. Pure Appl. Math., 53(2009), 21-36.
• [13] Cushing J.M., Levarge S., Chitnis N., Henson S.M., Some discrete competition models and the competitive exclusion principle, J. Difference Equ. Appl., 10(2004), 1139-1152.
• [14] Kocic V.L., Ladas G., Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
• [15] Kulenović M.R.S., Merino O., Competitive-exclusion versus competitivecoexistence for systems in the plane, Discrete Cont. Dynamical Syst. Ser. B, 6(2006), 1141-1156.