Stability Of A Syn- Ecosystem Consisting Of A   Prey-Predator And Host Commensal To The Prey (With Mortality Rate For The Prey)

N. SESHAGIRI RAO1, N. CH. PATTABHI RAMACHARYULU2

1. Faculty in Mathematics, Department of Humanities & Sciences

Tenali Engineering College, Tenali-522201, India. seshu.namana@gmail.com.

2. Former faculty, Department of Mathematics

National Institute of Technology, Warangal-506004, India

ABSTRACT:

          The present paper deals with a three species ecosystem consisting of a prey (N1), a predator (N2) and a host (N3) commensal to the prey having a mortality rate. The mathematical model equations constitute a set of three first order non-linear simultaneous equations in N1, N2 and N3. The equation for host is non-linear but de-coupled with the prey-predator pair. In all, there will be six equilibrium points of the model and the criteria for their stability are discussed. The trajectories of perturbations over the equilibrium states on species have been drawn.

 


International eJournal of Mathematics and Engineering

Volume 1, Issue 3, Pages 411 431