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Global Stability Analysis of a Three Level Ecological Ammensalism with Four Species

K.V.L.N.Acharyulu1 , N.Ch. Pattabhi Ramacharyulu2,P.Prasanna Anjaneyulu3 and  P. Rama Mohan4

1Department of Mathematics, Bapatla Engineering College, Bapatla - 522101, India, Email: kvlna@yahoo.com

2Dept. of Mathematics & Humanities, National Institute of Technology, Warangal – 506004, India

3Department of Mathematics, Vasireddy Venkatadri Institute of Technology, Nambur-522508, India.

4Department of Science and Humanities, St. Mary’s Engineering College, Chebrolu -522212, India.

ABSTRACT

This paper intends to investigate the global stability of a mathematical model of an ecological Ammensal model with Four Species (A,P,E,H)Eco-System of Ammensal-Prey(A),Predator-Ammensal(P),Enemy-Ammensal(E) and malice(M) species.This model is formed by establishing the System of an Ammensal –prey(A) , a Predator –Ammensal(P) that endures on Ammensal –prey(A), enemy-Ammensal(E)  and malice(M)  for which A, P are Ammensal respectively i.e., E and M adversely effect on A and P without themselves getting effected in any manner. Further E is Ammensal for M and M harms for E..The three levels of Ammensalism are comprised in the pairs of (A, E), (P, H) and (E,H).  The model is constituted with a set of four first order non-linear ordinary differential coupled equations.In this model, sixteen equilibrium points are obtained. Global stabiliy of this model is ascertained in the normal steady state.

Keywords: Ammensal, Prey, Predator, Enemy, Malice, Eco-System, Equillibrium point, stable.

AMS Classification: 92D25, 92D40

 

 

 

 


International eJournal of Mathematical Sciences, Technology and Humanities

Volume 2, Issue 5, Pages:  838 - 847