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:

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


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

i)     A constant number of S1 provided with reserve and

ii)   both the S1 and the S2 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