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Title: A mathematical model of four species syn-ecosymbiosis comprising of prey-predation, mutualism and commensalisms-I (Fully washed out state)
Authors: R. Srilatha, B. Ravindra Reddy, N. Ch. Pattabhiramacharyulu
Journal: ARPN Journal of Engineering and Applied Sciences
Publisher: Khyber Medical College, Peshawar
Country: Pakistan
Year: 2011
Volume: 6
Issue: 4
Language: English
This investigation deals with a mathematical model of a four species (S<sub>1,</sub> S<sub>2,</sub> S<sub>3 </sub>and S<sub>4</sub>) Syn-Ecological system (Fully Washed out State). S<sub>2 </sub>is a predator surviving on the prey S<sub>1</sub>: the prey is a commensal to the host S<sub>3</sub>which itself is in mutualism with the fourth species S<sub>4</sub>. S<sub>2</sub> and S<sub>4</sub> are neutral. The mathematical model equations characterizing the syn-ecosystem constitute a set of four first order non-linear coupled differential equations. There are in all sixteen equilibrium points. Criteria for the asymptotic stability of one of the sixteen equilibrium points: the fully washed out state is established. The linearised equations for the perturbations over the equilibrium point are analyzed to establish the criteria for stability. The system is noticed to be locally stable. Trajectories of the perturbations have been illustrated.
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