A trichotomy result for non-autonomous rational difference equations

• Autorzy: Frank Palladino , Michael Radin
• Języki publikacji: EN

Abstrakty

EN

We study non-autonomous rational difference equations. Under the assumption of a periodic non-autonomous parameter, we show that a well known trichotomy result in the autonomous case is preserved in a certain sense which is made precise in the body of the text. In addition we discuss some questions regarding whether periodicity preserves or destroys boundedness.

Słowa kluczowe

EN

Difference equation; Trichotomy; Non-autonomous; Periodic convergence; Global asymptotic stability

Kategorie tematyczne

• 39A10: Difference equations, additive

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 5
• Strony: 1135-1142

Daty

wydano

2011-10-01

online

2011-07-26

Twórcy

autor

Frank Palladino

• University of Rhode Island

autor

Michael Radin

• Rochester Institute of Technology

Bibliografia

• [1] Camouzis E., Ladas G., When does periodicity destroy boundedness in rational equations?, J. Difference Equ. Appl., 2006, 12(9), 961–979 http://dx.doi.org/10.1080/10236190600822369
• [2] Camouzis E., Ladas G., Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures, Adv. Discrete Math. Appl., 5, Chapman & Hall/CRC Press, Boca Raton, 2007 http://dx.doi.org/10.1201/9781584887669
• [3] Cushing J.M., Henson S.M., A periodically forced Beverton-Holt equation, J. Difference Equ. Appl., 2002, 8(12), 1119–1120 http://dx.doi.org/10.1080/1023619021000053980
• [4] Elaydi S., Sacker R.J., Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures, J. Difference Equ. Appl., 2005, 11(4–5), 337–346 http://dx.doi.org/10.1080/10236190412331335418
• [5] El-Metwally H.A., Grove E.A., Ladas G., A global convergence result with applications to periodic solutions, J. Math. Anal. Appl., 2000, 245(1), 161–170 http://dx.doi.org/10.1006/jmaa.2000.6747
• [6] Grove E.A., Kostrov Y., Ladas G., Schultz S.W., Riccati difference equations with real period-2 coefficients, Comm. Appl. Nonlinear Anal., 2007, 14(2), 33–56
• [7] Grove E.A., Ladas G., Periodicities in Nonlinear Difference Equations, Adv. Discrete Math. Appl., 4, Chapman & Hall/CRC Press, Boca Raton, 2005
• [8] Grove E.A., Ladas G., Predescu M., Radin M., On the global character of the difference equation \(x_{n + 1} = \frac{{\alpha + \gamma x_n - (2k + 1) + \delta x_{n - 2l} }} {{A + x_{n - 2l} }} \) , J. Difference Equ. Appl., 2003, 9(2), 171–199 http://dx.doi.org/10.1080/1023619021000054015
• [9] Karakostas G.L., Stević S., On the recursive sequence \(x_{n + 1} = B + \frac{{x_{n - k} }} {{a_0 x_n + \cdots + a_{k - 1} x_{n - k + 1} + \gamma }} \) , J. Difference Equ. Appl., 2004, 10(9), 809–815 http://dx.doi.org/10.1080/10236190410001659732
• [10] Kocić V.L., Ladas G., Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Math. Appl., 256, Kluwer, Dordrecht, 1993
• [11] Kulenovic M.R.S., Merino O., Stability analysis of Pielou’s equation with period-two coefficient, J. Difference Equ. Appl., 2007, 13(5), 383–406 http://dx.doi.org/10.1080/10236190601045929
• [12] Palladino F.J., Difference inequalities, comparison tests, and some consequences, Involve, 2008, 1(1), 91–100 http://dx.doi.org/10.2140/involve.2008.1.91
• [13] Palladino F.J., On the characterization of rational difference equations, J. Difference Equ. Appl., 2009, 15(3), 253–260 http://dx.doi.org/10.1080/10236190802119903
• [14] Palladino F.J., On periodic trichotomies, J. Difference Equ. Appl., 2009, 15(6), 605–620 http://dx.doi.org/10.1080/10236190802258677
• [15] Stevic S., Behavior of the positive solutions of the generalized Beddington-Holt equation, Panamer. Math. J., 2000, 10(4), 77–85
• [16] Stevic S., On the recursive sequence x n+1 = α n + x n−1/x n. II, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 2003, 10(6), 911–916
• [17] Stevic S., A short proof of the Cushing-Henson conjecture, Discrete Dyn. Nat. Soc., 2006, ID 37264
• [18] Stevic S., On positive solutions of a (k + 1)th order difference equation, Appl. Math. Lett., 2006, 19(5), 427–431 http://dx.doi.org/10.1016/j.aml.2005.05.014

Identyfikatory

DOI

10.2478/s11533-011-0066-3