Review of a predator-prey model with two limit cycles

dc.contributor.authorVan der Hoff, Quay
dc.contributor.authorHarding, Ansie
dc.contributor.emailquay.vanderhoff@up.ac.zaen_ZA
dc.date.accessioned2018-09-13T07:30:34Z
dc.date.issued2018
dc.description.abstractIt is well-known that the Lotka–Volterra predator-prey model has a family of periodic orbits, but does not possess limit cycles and therefore the model is said to be structurally unstable. The Lotka–Volterra model is a special case of a much larger group namely the quadratic population models and it can be shown that none of them can produce limit cycles. The surprising finding is that by combining two quadratic models a quadratic population model with two limit cycles is uncovered. Although the model looks simple at first glance it provides a rich source of dynamics and deserves attention. In this paper, we revisit a model that has its origin in the work of Dubois and Closset. A set of two quadratic population models interact as piecewise defined differential equations. The model has been discussed by Ren Yongtai and Han Li, cryptically written and showing some linguistic and typographical errors, but providing an excellent vehicle for developing skills in mathematical modelling, differential equations and technology for the young researcher. We explore the model in clearer detail and supplement the theory with rich graphical illustration. The paper has the purpose of providing an example of how a young researcher, such as a postgraduate student in biomathematics, can expand on an existing model by making use of current technology.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.embargo2019-08-20
dc.description.librarianhj2018en_ZA
dc.description.urihttp://www.tandfonline.com/loi/tmes20en_ZA
dc.identifier.citationQ. van der Hoff & A. Harding (2018): Review of a predator-prey model with two limit cycles, International Journal of Mathematical Education in Science and Technology, DOI: 10.1080/0020739X.2018.1510553. NYP.en_ZA
dc.identifier.issn0020-739X (print)
dc.identifier.issn1464-5211 (online)
dc.identifier.other10.1080/0020739X.2018.1510553
dc.identifier.urihttp://hdl.handle.net/2263/66553
dc.language.isoenen_ZA
dc.publisherTaylor and Francisen_ZA
dc.rights© 2018 Informa UK Limited, trading as Taylor & Francis Group. This is an electronic version of an article published in International Journal of Mathematical Education in Science and Technology, vol. , no. , pp. , 2018. doi : 10.1080/0020739X.2018.1510553. International Journal of Mathematical Education in Science and Technology is available online at : http://www.tandfonline.comloi/tmes20.en_ZA
dc.subjectQuadratic population modelen_ZA
dc.subjectBiomath educationen_ZA
dc.subjectLimit cyclesen_ZA
dc.subjectPiecewise-defined differential equationsen_ZA
dc.titleReview of a predator-prey model with two limit cyclesen_ZA
dc.typePostprint Articleen_ZA

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