Discrete Dynamics in Nature and Society

Discrete Dynamics in Nature and Society / 2004 / Article

Open Access

Volume 2004 |Article ID 946020 | https://doi.org/10.1155/S1026022604310010

Lin-Lin Wang, Wan-Tong Li, "Periodic solutions and stability for a delayed discrete ratio-dependent predator-prey system with Holling-type functional response", Discrete Dynamics in Nature and Society, vol. 2004, Article ID 946020, 19 pages, 2004. https://doi.org/10.1155/S1026022604310010

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

Received01 Oct 2003

Abstract

The existence of positive periodic solutions for a delayed discrete predator-prey model with Holling-type-III functional response N1(k+1)=N1(k)exp{b1(k)a1(k)N1(k[τ1])α1(k)N1(k)N2(k)/(N12(k)+m2N22(k))}, N2(k+1)=N2(k)exp{b2(k)+α2(k)N12(k[τ2])/(N12(k[τ2])+m2N22(k[τ2]))} 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.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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