%0 Journal Article
%T Effects of Additional Foods to Predators on Nutrient-Consumer-Predator Food Chain Model
%A Banshidhar Sahoo
%J ISRN Biomathematics
%D 2012
%R 10.5402/2012/796783
%X We have proposed a nutrient-consumer-predator model with additional food to predator, at variable nutrient enrichment levels. The boundedness property and the conditions for local stability of boundary and interior equilibrium points of the system are derived. Bifurcation analysis is done with respect to quality and quantity of additional food and consumer¡¯s death rate for the model. The system has stable as well as unstable dynamics depending on supply of additional food to predator. This model shows that supply of additional food plays an important role in the biological controllability of the system. 1. Introduction The interactions between living and nonliving organisms have significant role in ecological modelling. In every ecosystem, there always have been material fluxes from the outside to the system as well as from the system to outside. In a hypothetical steady state, these nutrient inputs and outputs balance. Many mathematical models have included these interactions. Effects of nutrient enrichment on a food chain model have been investigated, both empirically as well as theoretically by many scientists [1¨C3]. These nutrients enrichment may reduce species diversity and ecosystem functioning [4]. Also, many researchers [5¨C7] have shown that nutrient enrichment can lead to a complex dynamics as well as extinctions of species. In the late 1970s, Pimm and Lawton [8] simulated a large number of food webs including omnivorous links, as nonlinear interactions. They discovered that these additional interactions in general stable internal equilibria to become statistically rare. The role of additional food as a tool in biological control programs has become a topic of great attention for many scientists due to its ecofriendly nature. In recent years, many biologists, experimentalists, and theoreticians have concentrated on investigating the effects of providing additional food to predators in a predator-prey system [9¨C14]. Srinivasu et al. [12] have studied qualitative behavior of a predator-prey system in the presence of additional food to the predators, and they concluded that handling times for the available foods to the predator play a key role in determining the state of the ecosystem. In the controllability studies by Srinivasu et al. [12], it is observed that, for properly chosen quality and quantity of the additional food, the asymptotic state of a solution of the system can either be an equilibrium or a limit cycle. Sahoo and Poria [13] discussed the dynamic behaviour for seasonal effects on additional food in a predator-prey model. Very
%U http://www.hindawi.com/journals/isrn.biomathematics/2012/796783/