Stability Of A Syn- Ecosystem Consisting Of A Prey-Predator And Host Commensal To The Prey (With Predator Mortality Rate)
N.SESHAGIRI RAO1 and N. Ch. PATTABHI RAMACHARYULU2
1. Faculty in Mathematics, Department of Humanities & Sciences, Tenali Engineering College, Tenali-522201, India.
2. Former faculty, Department of Mathematics, National Institute of Technology, Warangal-506004, India.
The present paper deals with a three species ecosystem consisting of a prey (S1), a predator (S2) and a host (S3) commensal to the prey with mortality rate for predator. The mathematical model equations constitute a set of three first order non-linear simultaneous equations in the strengths N1, N2 and N3 of S1, S2 and S3 .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 on perturbations over the equilibrium states on species have been drawn.
Keywords: Equilibrium point, Equilibrium state, Stability, Carrying capacity, Reversal time of dominance.
International eJournal of Mathematics and Engineering
Volume 1, Issue 4, Pages: 535 – 553