Open AccessA dynamic reaction model of a prey-predator system with stage-structure for predator
Author(s) -
Tapan Kumar Kar,
Saroj Kumar Chattopadhyay
Publication year - 2010
Publication title -
modern applied science
Language(s) - English
Resource type - Journals
eISSN - 1913-1852
pISSN - 1913-1844
DOI - 10.5539/mas.v4n5p183
Subject(s) - predator , pontryagin's minimum principle , predation , stability (learning theory) , stage (stratigraphy) , control theory (sociology) , maximum principle , biomass (ecology) , mathematics , unit (ring theory) , mathematical optimization , ecology , computer science , optimal control , biology , control (management) , paleontology , mathematics education , machine learning , artificial intelligence
In this paper, we have considered a prey-predator model with stage-structure for predator and selective harvesting of prey species. A regulatory agency controls exploitation by imposing a tax per unit biomass of the prey species. The existence of steady states and their stability are studied. The problem of optimal harvesting policy is solved by using Pontryagin's maximal principle. It is also shown that time delay may cause a stable equilibrium to become unstable. Finally, some numerical simulations are carried out.