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August  2004, 4(3): 695-704. doi: 10.3934/dcdsb.2004.4.695

A continuous density Kolmogorov type model for a migrating fish stock

Kjartan G. Magnússon 1, , Sven Th. Sigurdsson 1, , Petro Babak 1, , Stefán F. Gudmundsson 1, and  Eva Hlín Dereksdóttir 1,

1. 

Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavík, Iceland, Iceland, Iceland, Iceland, Iceland

Received  January 2003 Revised  January 2004 Published  May 2004

A continuous probability density model for the spatial distribution and migration pattern for a pelagic fish stock is described. The model is derived as the continuum limit of a random walk in the plane which leads to an advection-diffusion equation. The direction of the velocity vector is given by the gradient of a "comfort function" which incorporates factors such as temperature, food density, distance to spawning grounds, etc., which are believed to affect the behaviour of the capelin. An application to Barents Sea capelin is presented.
Keywords: Kolmogorov equation, fish migration., random walk.
Mathematics Subject Classification: 92D25, 92D50, 35Q8.
Citation: Kjartan G. Magnússon, Sven Th. Sigurdsson, Petro Babak, Stefán F. Gudmundsson, Eva Hlín Dereksdóttir. A continuous density Kolmogorov type model for a migrating fish stock. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 695-704. doi: 10.3934/dcdsb.2004.4.695
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