American Institute of Mathematical Sciences

Advanced
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 and Continuous Dynamical Systems - B, 2004, 4 (3) : 695-704. doi: 10.3934/dcdsb.2004.4.695
[1]

Wafa Hamrouni, Ali Abdennadher. Random walk's models for fractional diffusion equation. Discrete and Continuous Dynamical Systems - B, 2016, 21 (8) : 2509-2530. doi: 10.3934/dcdsb.2016058
[2]

Edward Belbruno. Random walk in the three-body problem and applications. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : 519-540. doi: 10.3934/dcdss.2008.1.519
[3]

Brendan Weickert. Infinite-dimensional complex dynamics: A quantum random walk. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 517-524. doi: 10.3934/dcds.2001.7.517
[4]

Samuel Herrmann, Nicolas Massin. Exit problem for Ornstein-Uhlenbeck processes: A random walk approach. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 3199-3215. doi: 10.3934/dcdsb.2020058
[5]

Pablo D. Carrasco, Túlio Vales. A symmetric Random Walk defined by the time-one map of a geodesic flow. Discrete and Continuous Dynamical Systems, 2021, 41 (6) : 2891-2905. doi: 10.3934/dcds.2020390
[6]

Kumiko Hattori, Noriaki Ogo, Takafumi Otsuka. A family of self-avoiding random walks interpolating the loop-erased random walk and a self-avoiding walk on the Sierpiński gasket. Discrete and Continuous Dynamical Systems - S, 2017, 10 (2) : 289-311. doi: 10.3934/dcdss.2017014
[7]

Tomás Caraballo, Renato Colucci, Xiaoying Han. Semi-Kolmogorov models for predation with indirect effects in random environments. Discrete and Continuous Dynamical Systems - B, 2016, 21 (7) : 2129-2143. doi: 10.3934/dcdsb.2016040
[8]

Nguyen Huu Du, Nguyen Hai Dang. Asymptotic behavior of Kolmogorov systems with predator-prey type in random environment. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2693-2712. doi: 10.3934/cpaa.2014.13.2693
[9]

Antoine Conze, Nicolas Lantos, Olivier Pironneau. The forward Kolmogorov equation for two dimensional options. Communications on Pure and Applied Analysis, 2009, 8 (1) : 195-208. doi: 10.3934/cpaa.2009.8.195
[10]

Tracy L. Stepien, Hal L. Smith. Existence and uniqueness of similarity solutions of a generalized heat equation arising in a model of cell migration. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3203-3216. doi: 10.3934/dcds.2015.35.3203
[11]

Wolfgang Wagner. A random cloud model for the Wigner equation. Kinetic and Related Models, 2016, 9 (1) : 217-235. doi: 10.3934/krm.2016.9.217
[12]

Luigi Ambrosio, Luis A. Caffarelli, A. Maugeri. Preface: A beautiful walk in the way of the understanding. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : i-vi. doi: 10.3934/dcds.2011.31.4i
[13]

Eric A. Carlen, Maria C. Carvalho, Amit Einav. Entropy production inequalities for the Kac Walk. Kinetic and Related Models, 2018, 11 (2) : 219-238. doi: 10.3934/krm.2018012
[14]

Jianhai Bao, Xing Huang, Chenggui Yuan. New regularity of kolmogorov equation and application on approximation of semi-linear spdes with Hölder continuous drifts. Communications on Pure and Applied Analysis, 2019, 18 (1) : 341-360. doi: 10.3934/cpaa.2019018
[15]

Julien Dambrine, Nicolas Meunier, Bertrand Maury, Aude Roudneff-Chupin. A congestion model for cell migration. Communications on Pure and Applied Analysis, 2012, 11 (1) : 243-260. doi: 10.3934/cpaa.2012.11.243
[16]

Tzong-Yow Lee and Fred Torcaso. Wave propagation in a lattice KPP equation in random media. Electronic Research Announcements, 1997, 3: 121-125.

[17]

Dan Stanescu, Benito Chen-Charpentier. Random coefficient differential equation models for Monod kinetics. Conference Publications, 2009, 2009 (Special) : 719-728. doi: 10.3934/proc.2009.2009.719
[18]

Wolfgang Wagner. A random cloud model for the Schrödinger equation. Kinetic and Related Models, 2014, 7 (2) : 361-379. doi: 10.3934/krm.2014.7.361
[19]

Julia Calatayud, Juan Carlos Cortés, Marc Jornet. On the random wave equation within the mean square context. Discrete and Continuous Dynamical Systems - S, 2022, 15 (2) : 409-425. doi: 10.3934/dcdss.2021082
[20]

John Hubbard, Yulij Ilyashenko. A proof of Kolmogorov's theorem. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 367-385. doi: 10.3934/dcds.2004.10.367

2021 Impact Factor: 1.497

Tools

Metrics

  • PDF downloads (111)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy