A Distributed Delay Model With a Prey, Predator and Competitor
N V S R C Murty Gamini1, Paparao. A.V.2

1N V S R C Murty Gamini, Department of S & H, BVCITS, Batlapalem, Amalapuram (Andhra Pradesh), India.
2Paparao. A.V., Department of Mathematics, JNTUK, UCE Vizianagaram (Andhra Pradesh), India.
Manuscript received on 14 May 2019 | Revised Manuscript received on 19 May 2019 | Manuscript Published on 23 May 2019 | PP: 1992-1999 | Volume-7 Issue-6S5 April 2019 | Retrieval Number: F13590476S519/2019©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: In this paper we tend to study the stability analysis of prey(N1) ,predator(N2) and competitor(N3) model. Here competitor is vying with prey and is neutral with the predator. Besides that, the carrying capacities and the death rates relating to all the three species are also considered for investigation. The delay arguments are introduced in the interaction between prey and competitor species. The model is studied by a couple of integro-differential equations. The axial equilibrium point is known and local stability is studied at this point. Global stability analysis is carried out at this point by constructing appropriate lyapunov’s function. Further the system with delay and without delay arguments are compared by choosing suitable parameters and delay arguments further stabilize or destabilize the system is shown by aid of MATLAB simulation.
Keywords: Prey, Predator, Competitor Equilibrium Point, Local and Global Stability, Numerical Simulation Mathematical Classification: 34DXX.
Scope of the Article: Probabilistic Models and Methods