**InternationaleJournals**

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

**K.V.L.N.Acharyulu ^{1
}_{, }N.Ch. Pattabhi
Ramacharyulu^{2},P.Prasanna
Anjaneyulu^{3 }**

^{1}Department of
Mathematics, Bapatla Engineering College, Bapatla - 522101, India,

^{2}Dept. of Mathematics &
Humanities, National Institute of Technology,

^{3}Department of Mathematics, Vasireddy Venkatadri Institute of Technology,

^{4}Department
of Science and Humanities, St.
Mary’s Engineering College,

**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