×

zbMATH — the first resource for mathematics

Existence and stability of periodic orbits of periodic difference equations with delays. (English) Zbl 1154.39002
The authors investigate the existence and stability of periodic orbits of the \(p\)-periodic difference equation with delays \(x_n= f(n- 1,x_{n-k})\). It is shown that the periodic orbits of this equation depend on the periodic orbits of \(p\) autonomous equations when \(p\) divides \(k\). When \(p\) is not a divisor of \(k\), the periodic orbits depend on the periodic orbits of \(\text{gcd}(p, k)\) nonautonomous \(p/\text{gcd}(p, k)\)-periodic difference equation.
MSC:
39A11 Stability of difference equations (MSC2000)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1016/j.amc.2005.12.016 · Zbl 1109.90010 · doi:10.1016/j.amc.2005.12.016
[2] DOI: 10.1016/j.jmaa.2005.04.059 · Zbl 1125.39001 · doi:10.1016/j.jmaa.2005.04.059
[3] DOI: 10.1080/1023619021000047789 · Zbl 1030.39005 · doi:10.1080/1023619021000047789
[4] Beverton R. J. H., On the Dynamics of Exploited Fish Populations (2004)
[5] DOI: 10.1080/10236190108808308 · Zbl 1002.39003 · doi:10.1080/10236190108808308
[6] DOI: 10.1080/1023619021000053980 · Zbl 1023.39013 · doi:10.1080/1023619021000053980
[7] der Heiden U., Discr. Contin. Dyn. Syst. 11 pp 599–
[8] DOI: 10.1007/BF03167337 · Zbl 1306.39003 · doi:10.1007/BF03167337
[9] DOI: 10.2307/2974928 · Zbl 0893.58024 · doi:10.2307/2974928
[10] Elaydi S., Discrete Chaos (1999)
[11] DOI: 10.1080/10236190290027666 · Zbl 1048.39002 · doi:10.1080/10236190290027666
[12] Elaydi S., An Introduction to Difference Equations (2005) · Zbl 1071.39001
[13] DOI: 10.1016/j.jde.2003.10.024 · Zbl 1067.39003 · doi:10.1016/j.jde.2003.10.024
[14] DOI: 10.1080/10236190412331335418 · Zbl 1084.39005 · doi:10.1080/10236190412331335418
[15] DOI: 10.1016/S0022-247X(03)00417-7 · Zbl 1035.37020 · doi:10.1016/S0022-247X(03)00417-7
[16] DOI: 10.1080/10236190412331335436 · Zbl 1068.92038 · doi:10.1080/10236190412331335436
[17] DOI: 10.1016/S0167-2789(99)00231-6 · Zbl 0957.37018 · doi:10.1016/S0167-2789(99)00231-6
[18] DOI: 10.1007/978-94-017-1703-8 · doi:10.1007/978-94-017-1703-8
[19] DOI: 10.1080/10236190412331335463 · Zbl 1084.39007 · doi:10.1080/10236190412331335463
[20] DOI: 10.1080/10236190412331335472 · Zbl 1067.92048 · doi:10.1080/10236190412331335472
[21] DOI: 10.1017/CBO9780511608520 · Zbl 1060.92058 · doi:10.1017/CBO9780511608520
[22] DOI: 10.1080/1023619021000040489 · doi:10.1080/1023619021000040489
[23] DOI: 10.1038/261459a0 · Zbl 1369.37088 · doi:10.1038/261459a0
[24] DOI: 10.1139/f54-039 · doi:10.1139/f54-039
[25] DOI: 10.1016/S0167-2789(01)00324-4 · Zbl 1018.37047 · doi:10.1016/S0167-2789(01)00324-4
[26] Sharkovsky A. N., Ukrain. Math. Zh. 16 pp 61–
[27] DOI: 10.1017/CBO9780511987045 · doi:10.1017/CBO9780511987045
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.