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Stability Analysis of Host-mortal Commensal Eco-System with a Constant Harvesting of both the

Commensal and the Host

 

N. Seshagiri Rao1, K. Kalyani2  &  N.Ch. Pattabhi Ramacharyulu3

 

1, 2 Faculty in Mathematics, Department of Sciences & Humanities, Tenali Engineering College, Tenali-522201, India.

3  Former faculty, Department of Mathematics, National Institute of Technology, Warangal-506004, India.

 

Abstract:

In this paper we present a two species commensal interaction with limited resources and both the species are harvested at a constant rate where as the commensal species has a Mortality rate. The growth rate equations of this model are characterized by first order non-linear ordinary differential equations. In all, nine equilibrium states are identified. Further, solutions for the linearized perturbed (over the equilibrium states) equations have been obtained and results illustrated. Further, some threshold results are stated followed by the identification of threshold regions through illustrations. Also, global stability is discussed by constructing a suitable Liapunovís function.

 

 


International eJournal of Mathematics and Engineering

Volume 2, Issue 3, Pages:  1046 - 1073