Asymptotic behaviors of a two prey one predator model with cooperation among the prey species in a stochastic environment
In this paper, a two prey and one predator model with logistic growth in prey species have been considered in presence of stochastic perturbation. The cooperation among the preys against predation is assumed. Necessary conditions for asymptotic behavior around the equilibrium points of its deterministic system with and without stochasticity have been discussed. Finally, to illustrate the analytical results, numerical simulations have been performed.
KeywordsPredator–prey model Boundedness Global asymptotic stability Ito’s formula Stationary distribution Ergodicity
Mathematics Subject Classification37A30 37A50 92B05
We thank the anonymous referee for valuable suggestions to improve the article. Soumen Kundu thankful to DST, New Delhi, India, for its financial support under INSPIRE fellowship, without which this research would not have been possible.
- 16.May, R.M.: Stability and Complexity in model Ecosystem. Princeton University Press, Princeton (2001)Google Scholar
- 24.Begon, M., Harper, J.L., Townsend, C.R.: Ecology, Individuals, Populations and Communities. Blackwell Scientific Publications, Oxford (1986)Google Scholar
- 26.Janzen, D.: The natural history of mutualisms. In: The Biology of Mutualism: Ecology and Evolution, pp. 40–99 (1985)Google Scholar
- 27.Morin, P.J.: Community Ecology. Wiley, New York (2009)Google Scholar
- 34.Arnold, L.: Stochastic Differential Equations: Theory and Applications. Wiley, New York (1972)Google Scholar