Optimality and Sustainability of Delayed Impulsive Harvesting

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dc.contributor.advisorBraverman, Elena
dc.contributor.authorLawson, Jennifer Lynn
dc.contributor.committeememberLiao, Wenyuan
dc.contributor.committeememberRios, Cristian
dc.contributor.committeememberPost, John Robert
dc.date2022-11
dc.date.accessioned2022-07-22T18:35:04Z
dc.date.available2022-07-22T18:35:04Z
dc.date.issued2022-07-18
dc.description.abstractOptimal and sustainable management of natural resources requires knowledge about the behaviour of mathematical models of harvesting under many different types of conditions. In this thesis, the effects of delays on the optimality and sustainability of harvesting models are studied, with a particular focus on delayed impulsive harvesting models. We begin by considering delays within a continuous harvesting model and derive sufficient conditions for stability of harvesting models with general growth and harvesting rate. We also derive maximum sustainable yields for models with both logistic and Gompertz growth, and show that they are delay dependent. Then we consider the main object of the thesis, a logistic differential equation subject to impulsive delayed harvesting, where the deduction information is a function of the population size at the time of one of the previous impulses. A close connection to the dynamics of high-order difference equations is used to conclude that while the inclusion of a delay in the impulsive condition does not impact the optimality of the yield, sustainability may be highly affected and is once again delay-dependent. Maximum and other types of yields are explored, and sharp stability tests are obtained for the model, as well as explicit sufficient conditions. It is also shown that persistence of the solution is not guaranteed for all positive initial conditions, and extinction in finite time is possible, as is illustrated in the simulations. The results of this thesis imply that delays within harvesting should be kept short to maintain the sustainability of resources.en_US
dc.identifier.citationLawson, J. L. (2022). Optimality and Sustainability of Delayed Impulsive Harvesting (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.urihttp://hdl.handle.net/1880/114867
dc.identifier.urihttps://dx.doi.org/10.11575/PRISM/39928
dc.language.isoengen_US
dc.publisher.facultyScienceen_US
dc.publisher.institutionUniversity of Calgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en_US
dc.subjectDelaysen_US
dc.subjectImpulsive Harvestingen_US
dc.subjectOptimal Harvestingen_US
dc.subjectLogistic Equationen_US
dc.subjectImpulsive Delayed Harvestingen_US
dc.subjectPopulation Dynamicsen_US
dc.subject.classificationEducation--Mathematicsen_US
dc.titleOptimality and Sustainability of Delayed Impulsive Harvestingen_US
dc.typemaster thesisen_US
thesis.degree.disciplineMathematics & Statisticsen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameMaster of Science (MSc)en_US
ucalgary.item.requestcopytrueen_US
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