The dynamics of xn+1 = α+βxn/A+Bxn+Cxn-1 facts and conjectures

Computers and Mathematics with Applications

Volumn 45, Issue 6-9, 2003, Pages 1087-1099

  Kulenovic M R S ^a   Ladas, G ^a   Martins, L F ^b   Rodrigues, I W ^b  

^a University of Rhode Island   (United States)

^b CLEVELAND STATE UNIVERSITY   (United States)

Author keywords

Boundedness; Difference equation; Global asymptotic stability; Invariant intervals; Periodic solutions; Semicycles

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; LINEARIZATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

BOUNDEDNESS; CONJECTURES; GLOBAL ASYMPTOTIC STABILITY; INVARIANT INTERVALS; PERIODIC SOLUTIONS; SEMICYCLES;

DIFFERENCE EQUATIONS;

EID: 0037732763     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(03)00090-7     Document Type: Article

References (20)

1. n, J. Math. Anal. Appl. 233, 790-798, (1999).
2. n-1 Proceedings of WCNA2000, Catania, Italy, July 19-26, 2000, Nonlin. Anal. TMA 47, 4603-4614, (2001).
3. n Math. Sci. Res. Hot-Line 4 (2), 1-11, (2000).
4. n-1, In Proceedings of the First International Conference on Difference Equations and Applications, San Antonio, TX, May 25-28, 1994, Gordon and Breach Science, (1995).
5. V.L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic, Dordrecht, (1993).
6. V.L. Kocic, G. Ladas and I.W. Rodrigues, On the rational recursive sequences, J. Math. Anal. Appl. 173, 127-157, (1993).
7. V.L. Kocic, G. Ladas, G. Tzanetopoulos, and E. Thomas, On the stability of Lyness' equation, Discrete and Impulsive Systems 1, 245-254, (1995).
8. n, J. Differ. Equations Appl. 6 (5), 563-576, (2000).
9. M.R.S. Kulenović, G. Ladas and N.R. Prokup, A rational difference equation, Computers Math. Applic. 41 (5/6), 671-678, (2001).
10. n-1 , Math. Sci. Res. Hot-Line 2 (5), 1-16, (1998).
11. S. Kuruklis and G. Ladas, Oscillation and global attractivity in a discrete delay logistic model, Quart. Appl. Math. 50, 227-233, (1992).
12. U. Krause, Stability trichotomy, path stability, and relative stability for positive nonlinear difference equations of higher order, J. Diff. Equa. Appl. 1, 323-346, (1995).
13. R. Agarwal, Difference Equations and Inequalities. Theory, Methods and Applications, Marcel Dekker, New York, (1992).
14. S. Elaydi, An Introduction to Difference Equations, Second Edition, Springer-Verlag, New York, (1999).
15. E.A. Grove, G. Ladas, L.C. McGrath and C.T. Teixeira, Existence and behavior of solutions of a rational system, Comm. Appl. Nonlinear Anal. 8, 1-25, (2001).
16. W.G. Kelley and A. C. Peterson, Difference Equations, Academic Press, (1991).
17. Ch.G. Philos, I.K. Purnaras and Y.G. Sficas, Global attractivity in a nonlinear difference equation, Appl. Math. Comput. 62, 249-258, (1994).
18. M.R.S. Kulenović, Invariants and related Liapunov functions for difference equations, Appl. Math. Lett. 13 (7), 1-8, (2000).
19. M.R.S. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations, Chapman & Hall/CRC Press, Boca Raton, FL, (2001).
20. G. Ladas, Open problems and conjectures, J. Diff. Equa. Appl. 1 (3), 317-321, (1995).