
1135SFishHarvesting
08 Aug 2021   Contributor(s):: Jennifer Crodelle
This modeling scenario will introduce students to the concept of a bifurcation through a fish harvesting model. This short activity will walk students through a guided list of questions to help them to understand how the stability of equilibrium changes with changes in a model parameter, in this...

1127SFishHarvestingStudentVersion
06 May 2020   Contributor(s):: Will Mitchell
We offer students a harvesting model for operating a fishery over a 25 year horizon and ask them to write a report on optimal harvesting policy with their analyses for fishing industry experts (not necessarily mathematicians).

2017Biswasa, Haider Ali, Rajib Hossaina, and Mitun Kumar Mondala  Mathematical Modeling Applied to Sustainable Management of Marine Resources
27 Mar 2020   Contributor(s):: Brian Winkel
Biswasa, Haider Ali, Rajib Hossaina, and Mitun Kumar Mondala. 2017. Mathematical Modeling Applied to Sustainable Management of Marine Resources. Procedia Engineering. 194: 337 – 344. Abstract: In this work, we formulate and study a nonlinear mathematical model of...

2006Lingefjard, Thomas  Faces of mathematical modeling
25 Mar 2020   Contributor(s):: Brian Winkel
Lingefjard, Thomas. 2006. Faces of mathematical modeling. ZDM. 38(2): 96112.See https://subs.emis.de/journals/ZDM/zdm062a3.pdf .Abstract: In this paper I will discuss and exemplify my perspectives on how to teach mathematical modeling, as well as discuss quite different faces of...

2015Doust, Rahmani M.H. and Mansour Saraj  The logistic modeling population: having harvesting factor.
20 Mar 2020   Contributor(s):: Brian Winkel
Doust, Rahmani M.H. and Mansour Saraj. 2015. The logistic modeling population: having harvesting factor. Yugoslav Journal of Operations Research. 25(1): 107115.See http://elib.mi.sanu.ac.rs/files/journals/yjor/51/yujorn48p107115.pdf .Abstract: The present paper deals...

2013Bourne, Murray  Modeling fish stocks.
13 Mar 2020   Contributor(s):: Brian Winkel
Bourne, Murray. 2012. Modeling fish stocks. SquareCirclez The IntMath blog. See https://www.intmath.com/blog/mathematics/modelingfishstocks7377 .Mathematical modeling for better fish managementIt is possible to have a sustainable fishing industry with...

1143SPopulationModelVariationsMATLAB
17 Feb 2019   Contributor(s):: Bill Skerbitz
Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations. They will also work with other utilities...

1986Cook, K. L. and M. Witten  Onedimensional linear and logistic harvesting models.
09 Dec 2018   Contributor(s):: Brian Winkel
Cook, K. L. and M. Witten. 1986. Onedimensional linear and logistic harvesting models. Mathematical Modeling. 7: 301340.See https://core.ac.uk/download/pdf/81116076.pdf .Abstract: Some of the results in the literature on simple onedimensional, density dependent, discrete and...

2017Imane Agmour, Meriem Bentounsi, Naceur Achtaich, and Youssef El Foutayeni  Optimization of the Two Fishermen's Profits Exploiting Three Competing Species Where Prices Depend on Harvest
07 Mar 2018   Contributor(s):: Imane Agmour, Meriem Bentounsi, Naceur Achtaich, Youssef El Foutayeni
Imane Agmour, Meriem Bentounsi, Naceur Achtaich, and Youssef El Foutayeni. 2017. Optimization of the Two Fishermen’s Profits Exploiting Three Competing Species Where Prices Depend on Harvest. International Journal of Differential Equations. Volume 2017, Article ID 3157294, 17...

2018Unknown  The Logistic Differential Equation  Notes
03 Mar 2018   Contributor(s):: Brian Winkel
The Logistic Differential Equation. Notes. 7 pp.Goals from the notes:• MATH: To analyze the behavior of solutions of an ordinary differential equation geometrically .• MATH: To analyze stability behavior of equilibria of an ordinary differential equation geometricallyand...

2009Das, Tapasi, R. N. Mukherjee, and K. S. Chaurhur  Bioeconomic harvesting of a prepredator fishery.
03 Mar 2018   Contributor(s):: Tapasi Das
Das, Tapasi, R. N. Mukherjee, and K. S. Chaurhur. 2009. Bioeconomic harvesting of a prepredator fishery. Journal of Biological Dynamics. 3(5): 447462.See https://pubmed.ncbi.nlm.nih.gov/22880894/ . Abstract: This paper deals with the problem of nonselective harvesting of a...

2015Endale, Mersha Amdie  Some application of first order differential equations to real world system. Masters Thesis.
26 Nov 2017   Contributor(s):: Brian Winkel
Endale, Mersha Amdie. 2015. Some application of first order differential equations to real world system. Masters Thesis. Haramaya University.We quote from the opening by the author,“The subject of differential equations is important part of mathematics for understanding the...

2011Wentworth, Corinne, Masami Fujiwara, and Jay Walton  Optimal harvesting models for fishery populations.
12 Sep 2017   Contributor(s):: Brian Winkel
Wentworth, Corinne, Masami Fujiwara, and Jay Walton. 2011. Optimal harvesting models for fishery populations. REU paper. 17 pp.Abstract. Fishery management is the consideration of the ecological effects of harvesting. Fisherman work to provide fish for a growing human population...

2008Suri, Ratneesh  Optimal harvesting strategies for fisheries: a differential equations approach. PhD Thesis.
12 Sep 2017   Contributor(s):: Brian Winkel
Suri, Ratneesh. 2008. Optimal harvesting strategies for fisheries: a differential equations approach. PhD Thesis. 209 pp.This thesis considers how we might optimally harvest using logistic model with constant harvest to determine maximum sustainable yield and optimal economic...

2010Keesom, No'am , Trisha Macrae, Anjuli Uhlig, and Richard Wang  Fishing for Answers: Investigating Sustainable Harvesting Rate.
12 Sep 2017   Contributor(s):: Brian Winkel
Keesom, No’am , Trisha Macrae, Anjuli Uhlig, and Richard Wang. 2010. Fishing for Answers: Investigating Sustainable Harvesting Rate. Paper 11 pp.Abstract: The purpose of this report is to determine and propose a model by which an optimal harvesting frequency can be...

2013Idlango, Majda  Differential Equation Population Models in a Slowly Varying Environment. PhD Thesis.
12 Sep 2017   Contributor(s):: Brian Winkel
Idlango, Majda. 2013. Differential Equation Population Models in a Slowly Varying Environment. PhD Thesis. 181 pp.Summary: Many investigations have been carried out that analyse population dynamics using differential equations where the governing parameters of the models concerned are...

2009Unknown  Bifurcation Analysis
12 Sep 2017   Contributor(s):: Brian Winkel
2009. Bifurcation Analysis – One Dimensional ODEs. Notes. 11 pp.This document contains many rich illustrations of various kinds of bifurcation in the context of applications. E.g. harvesting, magnetometer, spruce budworm,Kywords: differential equation, model, bifurcation, analysis,...

2017Kallen, Anders  Single species models in continuous time
12 Sep 2017   Contributor(s):: Brian Winkel
Kallen, Anders. Single species models in continuous time. Lecture notes. 4 pp.http://www.maths.lth.se/matematiklth/personal/andersk/kurser/biomath2016/F4.pdf . Accessed 11 Septembe 2017.Part of a series of Lecture notes this lecture contains rich materials on logistic harvest...

2017Shi, Junping  Modeling Population Growth Single Species
12 Sep 2017   Contributor(s):: Brian Winkel
Shi, Junping. Modeling Population Growth Single Species. Activities Notes. 4 pp.This is a set of descriptions of various logistic models. Keywords: differential equation, model, harvest, Gompertz, Allee effect, constant harvest

2000Idels, Lev. V. and Mei Wang  Harvesting Fisheries Management Strategies With Modified Effort Function
12 Sep 2017   Contributor(s):: Brian Winkel
Idels, Lev. V. and Mei Wang. 2000. Harvesting Fisheries Management Strategies With Modified Effort Function. Int. J. Modelling, Identification and Control. Preprint.See https://arxiv.org/ftp/math/papers/0601/0601539.pdf .Abstract: In traditional harvesting model a fishing effort E is...