Differential Equations and Dynamical Systems

, Volume 27, Issue 4, pp 449–465 | Cite as

Persistence and Stability of a Seasonally Perturbed Three Species Stochastic Model of Salmonoid Aquaculture

  • Partha Ghosh
  • Pritha DasEmail author
  • Debasis Mukherjee
Original Research


Dynamics of a seasonally perturbed stochastic three species (phytoplankton-zooplankton-fish) system with harvesting is investigated in this article. The effect of periodic variations is considered on three different parameters of the system, growth rate of prey and mortality rates of middle and top predator. These seasonally varying parameters are considered to be in the different phases. Uniform boundededness of the system is proved. Existence of unique positive global solution of the system is established. It is observed that the system is strongly persistent in mean under certain parametric conditions. Gaussian white noise term is introduced into the system to represent the effect of random harvesting of fish population through poaching, uncontrolled recreational fishing or escape into wild habitat during storm. It is observed that the system is stable in mean square when the intensity of noise is small.


Seasonal variation White noise Persistence in mean Mean square stability 



The authors are grateful to the anonymous reviewers for their helpful comments and suggestions to improve the paper. We pay homage to Late Prof. A. B. Roy, Department of Mathematics, Jadavpur University, Kolkata, for his kind help and suggestions given before his demise in writing this article.


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Copyright information

© Foundation for Scientific Research and Technological Innovation 2016

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Engineering Science and TechnologyHowrahIndia
  2. 2.Department of MathematicsVivekananda CollegeKolkataIndia

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