THE ROLE OF DELAY IN DIGESTION OF PLANKTON BY FISH POPULATION A FISHERY MODEL

Volume 1, Issue 1, pp 13-19 http://dx.doi.org/10.22436/jnsa.001.01.03

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Authors

JOYDIP DHAR - Department of Applied Sciences, ABV-Indian Institute of Information Technology and Management, Gwalior-474 010, M.P, INDIA.. ANUJ KUMAR SHARMA - Department of Mathematics, L.R.D.A.V. College, Jagraon-142026, Ludhiana, Punjab, INDIA.. SANDEEP TEGAR - School of Mathematics and Allied Sciences, Jiwaji University, Gwalior- 474011, M.P., INDIA..

Abstract

In this Paper we have developed a model in which the revenue is generated from fishing and the growth of fish depends upon the plankton which in turn grows logistically. The conditions for the persistence of system around non zero equilibrium have been found out using average Liapnouv function after establishing existence and boundedness of the solution. Then we formulated a model with delay in digestion of plankton by fish. Further the the threshold value of conversional parameter has been found out for hopf-bifurcation. The phenomena of hopf-bifurcation is demonstrated using graphs.

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Keywords

• Fishery Model
• Stability
• Delay
• Hopf-bifurcation

MSC

•  92D30
•  92D40
•  37G15.

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