A Mathematical Model of Four Species Syn-Ecosymbiosis comprising of Prey-Predation, Mutualism and Commensalisms-II

(Three of the Four Species are Washed out States)

R. Srilatha1 and N. Ch. Pattabhiramacharyulu2

1JNTUH, Kukatpally, Hyderabad-500085, India.

2Faculty of Mathematics (Retd.), NIT, Warangal – 506004, India. E-mail:



This investigation deals with a mathematical model of a four species (S1, S2, S3 and S4)     Syn-Ecological system (Three of the four species are washed out states). S2 is a predator surviving on the prey S1: the prey is a commensal to the host S3 which itself is in mutualism with the fourth species S4. Further S2 and S4 are neutral. The model equations of the system constitute a set of four first order non-linear ordinary differential coupled equations.  In all, there are sixteen equilibrium points.  Criteria for the asymptotic stability of four of the sixteen equilibrium points: Three of the four species are washed out states only are established in this paper.  The linearized equations for the perturbations over the equilibrium points are analyzed to establish the criteria for stability and the trajectories illustrated.

Key words: Equilibrium state, stability, Mutualism, Commensalisms




International eJournal of Mathematics and Engineering

Volume 3, Issue 1, Pages:  1322 - 1330