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Abstract and Applied Analysis
Volume 2015, Article ID 241312, 7 pages
http://dx.doi.org/10.1155/2015/241312
Research Article

Birth Rate Effects on an Age-Structured Predator-Prey Model with Cannibalism in the Prey

1CIMAT, Jalisco, s/n, 36240 Col Valenciana, GTO, Mexico
2Universidad Autónoma de Aguascalientes, Edificio 26, Avenida Universidad No. 940, 20100 Aguascalientes, AGS, Mexico

Received 9 September 2014; Revised 15 December 2014; Accepted 16 December 2014

Academic Editor: Wanbiao Ma

Copyright © 2015 Francisco J. Solis and Roberto A. Ku-Carrillo. 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.

Abstract

We develop a family of predator-prey models with age structure and cannibalism in the prey population. It consists of systems of ordinary differential equations, where is a parameter associated with new proposed prey birth rates. We discuss how these new birth rates give the required flexibility to produce differential systems with well-behaved solutions. The main feature required in these models is the coexistence among the involved species, which translates mathematically into stable equilibria and periodic solutions. The search for such characteristics is based on heuristic predation functions that account for cannibalism in the prey.