August  2004, 4(3): 713-720. doi: 10.3934/dcdsb.2004.4.713

A general dynamical theory of foraging in animals

1. 

Oceanlab, School of Biological Sciences, University of Aberdeen, Newburgh, Ellon, Aberdeenshire, AB41 6AA, United Kingdom, United Kingdom

Received  December 2002 Revised  October 2003 Published  May 2004

This paper provides a minimally simple theory that accounts for the foraging behaviour of animals. It presents three separate systems of differential equations that predict the selection of diets from various types of food, and also the time-budgets of the occupancy of patches of food without, and with regeneration of food. The theory subsumes the whole of optimal foraging theory as one special case of foraging behaviour defined by the physiological requirements of animals. The theory explains foraging in terms of both the acquisition of food and the utilization of food in the maintenance of life.
Citation: J. G. Ollason, N. Ren. A general dynamical theory of foraging in animals. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 713-720. doi: 10.3934/dcdsb.2004.4.713
[1]

Mahin Salmani, P. van den Driessche. A model for disease transmission in a patchy environment. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 185-202. doi: 10.3934/dcdsb.2006.6.185

[2]

Alberto Bressan, Fabio S. Priuli. Nearly optimal patchy feedbacks. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 687-701. doi: 10.3934/dcds.2008.21.687

[3]

Bin-Guo Wang, Wan-Tong Li, Lizhong Qiang. An almost periodic epidemic model in a patchy environment. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 271-289. doi: 10.3934/dcdsb.2016.21.271

[4]

Qianqian Cui, Zhipeng Qiu, Ling Ding. An SIR epidemic model with vaccination in a patchy environment. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1141-1157. doi: 10.3934/mbe.2017059

[5]

Daozhou Gao, Yijun Lou, Shigui Ruan. A periodic Ross-Macdonald model in a patchy environment. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3133-3145. doi: 10.3934/dcdsb.2014.19.3133

[6]

Samuel Bernard, Fabien Crauste. Optimal linear stability condition for scalar differential equations with distributed delay. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 1855-1876. doi: 10.3934/dcdsb.2015.20.1855

[7]

Kuang-Hui Lin, Yuan Lou, Chih-Wen Shih, Tze-Hung Tsai. Global dynamics for two-species competition in patchy environment. Mathematical Biosciences & Engineering, 2014, 11 (4) : 947-970. doi: 10.3934/mbe.2014.11.947

[8]

Bin-Guo Wang, Wan-Tong Li, Liang Zhang. An almost periodic epidemic model with age structure in a patchy environment. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 291-311. doi: 10.3934/dcdsb.2016.21.291

[9]

Frank Pörner, Daniel Wachsmuth. Tikhonov regularization of optimal control problems governed by semi-linear partial differential equations. Mathematical Control & Related Fields, 2018, 8 (1) : 315-335. doi: 10.3934/mcrf.2018013

[10]

Jianhui Huang, Xun Li, Jiongmin Yong. A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon. Mathematical Control & Related Fields, 2015, 5 (1) : 97-139. doi: 10.3934/mcrf.2015.5.97

[11]

Yu Mu, Wing-Cheong Lo. Dynamics of the food-chain population in a polluted environment with impulsive input of toxicant. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020279

[12]

Ming Chen, Hao Wang. Dynamics of a discrete-time stoichiometric optimal foraging model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020264

[13]

Elimhan N. Mahmudov. Optimal control of evolution differential inclusions with polynomial linear differential operators. Evolution Equations & Control Theory, 2019, 8 (3) : 603-619. doi: 10.3934/eect.2019028

[14]

Jing Feng, Bin-Guo Wang. An almost periodic Dengue transmission model with age structure and time-delayed input of vector in a patchy environment. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020220

[15]

Vu Hoang Linh, Volker Mehrmann. Spectral analysis for linear differential-algebraic equations. Conference Publications, 2011, 2011 (Special) : 991-1000. doi: 10.3934/proc.2011.2011.991

[16]

Eugenia N. Petropoulou, Panayiotis D. Siafarikas. Polynomial solutions of linear partial differential equations. Communications on Pure & Applied Analysis, 2009, 8 (3) : 1053-1065. doi: 10.3934/cpaa.2009.8.1053

[17]

Leonid Berezansky, Elena Braverman. Stability of linear differential equations with a distributed delay. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1361-1375. doi: 10.3934/cpaa.2011.10.1361

[18]

Hui Liang, Hermann Brunner. Collocation methods for differential equations with piecewise linear delays. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1839-1857. doi: 10.3934/cpaa.2012.11.1839

[19]

Nguyen Dinh Cong, Doan Thai Son. On integral separation of bounded linear random differential equations. Discrete & Continuous Dynamical Systems - S, 2016, 9 (4) : 995-1007. doi: 10.3934/dcdss.2016038

[20]

Nizami A. Gasilov. Solving a system of linear differential equations with interval coefficients. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020203

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (26)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]