A bioeconomic model of a ratio-dependent predator-prey system and optimal harvesting

  • T. K. Kar
  • Swarnakamal Misra
  • B. Mukhopadhyay


This paper deals with the problem of a ratio-dependent prey-predator model with combined harvesting. The existence of steady states and their stability are studied using eigenvalue analysis. Boundedness of the exploited system is examined. We derive conditions for persistence and global stability of the system. The possibility of existence of bionomic equilibria has been considered. The problem of optimal harvest policy is then solved by using Pontryagin’s maximal principle.

AMS Mathematics Subject Classification

92D25 34K20 49K15 

Key words and phrases

Harvesting ratio-dependent permanence bionomic-equilibrium optimal harvesting 


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Copyright information

© Korean Society for Computational & Applied Mathematics and Korean SIGCAM 2006

Authors and Affiliations

  • T. K. Kar
    • 1
  • Swarnakamal Misra
    • 2
  • B. Mukhopadhyay
    • 1
  1. 1.Department of MathematicsBengal Engineering and Science UniversityShibpur, HowrahIndia
  2. 2.Department of MathematicsDhakuria Ram Chandra High SchoolDhakuria, KolkataIndia

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