Authors: M.A.S. Srinivas; A. Prasanthi; Y. Narasimhulu
Addresses: Department of Mathematics, Jawaharlal Nehru Technological University, Hyderabad, Telangana, India ' Department of Mathematics, Jawaharlal Nehru Technological University, Hyderabad, Telangana, India ' Academic Staff College, Hyderabad Central University, Hyderabad, Telangana, India
Abstract: In this paper we have considered prey-predator model, where both prey and predator have other food source and both are harvested with different catchability coefficients. Many researchers consider all the parameters of their models are given by fixed values (precise values). In this paper we consider the model with some of the parameters have impreciseness that is, they may assume any value in an interval. The discussion is made by defining an interval valued function. In this paper stability aspects, bionomic equilibrium and optimum harvesting policy are discussed. The paper also presents the stability when time delay is incorporated in the beneficial term of the predator growth equation. All the theoretical results are validated by the numerical simulations.
Keywords: interval numbers; stability; time delay; optimal control; Hopf bifurcation; bioeconomics; mathematical modelling; prey-predator models; imprecise parameters; uncertainty; interval valued function; bionomic equilibrium; harvesting policy; predator growth equation; numerical simulation.
International Journal of Mathematical Modelling and Numerical Optimisation, 2015 Vol.6 No.2, pp.114 - 140
Received: 22 Sep 2014
Accepted: 08 Mar 2015
Published online: 16 Jun 2015 *