Abstract
In this paper we have studied the stability of three typical species syn-ecosystem. The system comprises of one commensal S1 and two hosts S2 and S3 . Both S2 and S2 benefit S1 without getting themselves affected either positively or adversely. Further S2 is a commensal of S3 and S3 is a host of both S1 and S2. Limited resources have been considered for all the three species in this case. The model equations of the system constitute a set of three first order non-linear ordinary differential equations. The possible equilibrium points of the model are identified. We have also studied the local and global stabilities. We have analyzed the bionomic equilibrium and optimal harvesting strategy using Pontryagin’s maximum principle. We have investigated the inhabitant intensities of the fluctuations (variances) around the positive equilibrium due to noise and have investigated the stability. We have also checked the MATLAB numerical simulations for stability of the system.
Recommended Citation
Srinivas, M. N.; Sabarmathi, A.; Reddy, K. S.; and S. Srinivas, M. A.
(2014).
An Optimal Harvesting Strategy of a Three Species Syn-ecosystem with Commensalism and Stochasticity,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 9,
Iss.
2, Article 15.
Available at:
https://digitalcommons.pvamu.edu/aam/vol9/iss2/15
Included in
Biology Commons, Finance Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Physical Sciences and Mathematics Commons, Other Social and Behavioral Sciences Commons