**InternationaleJournals**

**Threshold Theorems Of Two -Species Competitive
Ecological Model with reserve for One Species and harvesting both Species at
rates proportional to their respective sizes**

**B.Bhaskara Rama
Sarma ^{1} &
N.Ch.Pattabhiramacharyulu ^{2}**

1.Faculty of Mathematics, BRS Classes, #2-284
,Vivekananda street,Hanumannagar,Ramavarappadu, Vijayawada, A.P-521108 ;

Mobile: 9441924418 ; E-mail: bbramasarma@yahoo.co.in

2.Faculty of Mathematics (Retd.), NIT, Warangal, A.P. – 506 004.

**ABSTRACT**

In the present investigation we study a two Species
competition model incorporating

i) A constant number of S_{1 }provided with
reserve and

ii) both the S_{1} and the S_{2}
are harvested proportional to their population sizes.

The model is characterized by a couple of first order
non-linear ordinary differential equations. All the four equilibrium points of
the model are identified and stability criteria are outlined.Some threshold
theorems have been derived for Normal steady
state and results are illustrated.

**Key words** :Model equations
, Stability ,Interactions,Equilibrium states, Threshold theorems

**AMS Classification**
: 92 D 25, 92 D 40

**International
eJournal of Mathematics and Engineering**

**Volume** 2,
**Issue** 2, **Pages**: 985 - 991