Acta mathematica scientia, Series B >
A GENERALIZED SEMICONJUGACY IN DIFFERENCE EQUATIONS
Received date: 2010-05-04
Revised date: 2010-10-24
Online published: 2012-05-20
Difference equations arise in many fields. This article is concerned to general-ization of semiconjugacy in difference equations. In fact, H. Sedaghat in [7] investigated the semiconjugacy in difference equations where the factor maps are one-dimensional. We gen-eralize the definition of semiconjugacy of maps, where the factor map is multi-dimensional. This generalization is very useful. By this generalization, we can investigate the dynamics of many difference equations especially the dynamics of systems of higher order difference equations. Some systems of difference equations are investigated using the semiconjugacy property.
Key words： Difference equation; generalized semiconjugacy; linked map; factor map
Reza Mazrooei-Sebdani , Mehdi Dehghan . A GENERALIZED SEMICONJUGACY IN DIFFERENCE EQUATIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(3) : 978 -988 . DOI: 10.1016/S0252-9602(12)60073-3
[1] Allen L J S. Some discrete-time SI, SIS, and SIR epidemic models. Math Biosciences, 1994, 124: 83–105
[2] Allen L J S, Burgin A B. Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math Biosciences, 2000, 163: 1–33
[3] Chan D M, Chang E R, Dehghan M, et al. Asymptotic stability for difference equations with decreasing arguments. J Diff Eq Applic, 2006, 12: 109–123
[4] Dehghan M, Kent C M, Mazrooei-Sebdani R, et al. Dynamics of rational difference equations containing quadratic terms. J Diff Eq Applic, 2008, 14: 191–208
[5] Kulenovic M R S, Ladas G. Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures. Boca Raton: Chapman and Hall/CRC, 2002
[6] Sedaghat H. Semiconjugates of One-dimensional Maps. J Diff Eq Applic, 2002, 8: 649–666
[7] Sedaghat H. Nolinear Difference Equations, Theory with Applications to Social Science Models. Dordrecht: Kluwer Academic Publishers, 2003
/
| 〈 |
|
〉 |