The Existence and Uniqueness of the Solution of a Diusive Predator-Prey Model with Omnivory and General Nonlinear Functional Response
Wensheng Yang *
College of Mathematics and Informatics, Fujian Normal University, Fuzhou, Fujian 350117, P. R. China. and FJKLMAA and Center for Applied Mathematics of Fujian province (FJNU), Fuzhou, Fujian 350117, P. R. China.
*Author to whom correspondence should be addressed.
Abstract
In this work, we consider a three species modified Lesie-Gower food web model with general nonlinear functional response and omnivory which is defined as feeding on more than one trophic level. The carrying capacity of the model is proportional to the population size of the biotic resource plus a const. The main objective of this paper is to investigate the existence and uniqueness of the solution of this model. It is shown that the omnivory has important influence on the existence and uniqueness of the solution of the model.
Keywords: Food web model, Biotic resource, Omnivory, Upper-lower solution, Semigroup.