Nonlinear Dynamics

, Volume 72, Issue 3, pp 591–603 | Cite as

Conservation of a resource based fishery through optimal taxation

  • U. K. Pahari
  • T. K. Kar
Original Paper


In the present paper, we study a dynamic reaction model in which (i) the predator is provided with an alternative food in addition to the prey species, (ii) the predator is harvested, and (iii) a tax is imposed to regulate the system. The existence of possible steady states along with their local as well as global stability is discussed for both the exploited and unexploited systems. Boundedness of the system is also discussed. It is seen that the system undergoes a Hopf bifurcation by the addition of alternative prey and the criteria for the Hopf-bifurcation is also discussed. Optimal tax policy is discussed using Pontryagin’s maximal principle. Finally, some numerical simulations are given to show the consistency with theoretical analysis.


Alternative prey Dynamic reaction Harvesting Global stability Bifurcation Taxation 



Research of U.K. Pahari was supported by the UGC, India (Grant No. F. PSW-180/09-10(ERO)).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsSree Chaitanya CollegeHabraIndia
  2. 2.Department of MathematicsBengal Engineering and Science UniversityHowrahIndia

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