Periodic solutions and stability for a delayed discrete ratio-dependent predator-prey system with Holling-type functional response

Lin-Lin Wang and Wan-Tong Li

Discrete Dynamics in Nature and Society, 2004, vol. 2004, 1-19

Abstract:

The existence of positive periodic solutions for a delayed discrete predator-prey model with Holling-type-III functional response N 1 ( k + 1 ) = N 1 ( k ) exp { b 1 ( k ) − a 1 ( k ) N 1 ( k − [ τ 1 ] ) − α 1 ( k ) N 1 ( k ) N 2 ( k ) / ( N 1 2 ( k ) + m 2 N 2 2 ( k ) ) } , N 2 ( k + 1 ) = N 2 ( k ) exp { − b 2 ( k ) + α 2 ( k ) N 1 2 ( k − [ τ 2 ] ) / ( N 1 2 ( k − [ τ 2 ] ) + m 2 N 2 2 ( k − [ τ 2 ] ) ) } is established by using the coincidence degree theory. We also present sufficient conditions for the globally asymptotical stability of this system when all the delays are zero. Our investigation gives an affirmative exemplum for the claim that the ratio-dependent predator-prey theory is more reasonable than the traditional prey-dependent predator-prey theory.

Date: 2004
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2004/946020.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2004/946020.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:946020

DOI: 10.1155/S1026022604310010

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().