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Lindström, T. (2019). Mathematics and Recurrent Population Outbreaks. In: Bharath Sriraman (Ed.), Handbook of the Mathematics of the Arts and Sciences: . Cham: Springer
Open this publication in new window or tab >>Mathematics and Recurrent Population Outbreaks
2019 (English)In: Handbook of the Mathematics of the Arts and Sciences / [ed] Bharath Sriraman, Cham: Springer, 2019Chapter in book (Refereed)
Abstract [en]

Despite that outbreaks had been observed for hundreds of years for many populations, it took until the 1920s before the first mechanisms that did not involve human interference were suggested. Just a few mechanisms were included in the first models and the question whether the inclusion of other, very plausible, mechanisms could alter the predictions remained. In this chapter, we follow the development of models that have been proposed to explain oscillatory population dynamics from the early models suggested by Lotka (1925) and Volterra (1926) until global dynamical questions that are still open for models incorporating explicit resource dynamics, like the chemostat, cf Kuang (1989).

Place, publisher, year, edition, pages
Cham: Springer, 2019
Keywords
Global stability ; Limit cycle ; Lyapunov function ; Mechanistic population models ; Oscillatory dynamics ; Recurrent outbreaks
National Category
Computational Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-79673 (URN)10.1007/978-3-319-70658-0_33-1 (DOI)978-3-319-70658-0 (ISBN)
Available from: 2019-01-21 Created: 2019-01-21 Last updated: 2019-05-16
Gyllenberg, M., Hanski, I. & Lindström, T. (2017). Conditional reproductive strategies under variable environmental conditions. Annales Zoologici Fennici, 54(1-4), 193-204
Open this publication in new window or tab >>Conditional reproductive strategies under variable environmental conditions
2017 (English)In: Annales Zoologici Fennici, ISSN 0003-455X, E-ISSN 1797-2450, Vol. 54, no 1-4, p. 193-204Article in journal (Refereed) Published
Abstract [en]

Within the framework of adaptive dynamics we consider the evolution by natural selection of reproductive strategies in which individualsmay adjust their reproductive behaviour in response to changing environmental conditions. As a specific example we consider a discrete-time model in which possible fluctuations in the environmental conditions are caused by predator-prey interaction. Our main findings include: 1) Coexistence between two fixed strategies (i.e., strategies that do not adjust to changing environmental conditions) is impossible. There exists a best fixed strategy, which invades and ousts all other fixed strategies. 2) A necessary condition for conditional (adjustable) strategies to evolve is that there are fluctuations in the environmental conditions. Predator-prey interactions may cause such fluctuations and under natural assumptions there exists an optimal conditional strategy which is uninvadable and invades and ousts allother strategies.

Keywords
adjustable strategy, environental conditions, adaptive dynamics
National Category
Other Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-63759 (URN)000401779600017 ()
Available from: 2017-05-11 Created: 2017-05-11 Last updated: 2017-07-19Bibliographically approved
Lindström, T. (2017). Med fokus på linjär algebra (3ed.). Lund: Studentlitteratur AB
Open this publication in new window or tab >>Med fokus på linjär algebra
2017 (Swedish)Book (Other academic)
Abstract [sv]

Den linjära algebran innehåller i dag ett rikt spektrum av metoder som används och en förståelse för dessa metoder krävs inom nästanalla samhällsområden som använder datorer, beräkningar,bildbehandling eller liknande. Även om verkligheten ofta är ickelinjär, så kräver icke-linjär analys ofta mycket god förståelse av de linjära specialfallen. Få delområden i matematiken kan på en lika elementär nivå klargöra skillnaderna mellan effektiva och mindre effektiva algoritmer och åskådliggöra vilken potential matematiken ger för en fortsatt samhällsutveckling.

Denna bok riktar sig till den grupp av studenter, som behöverkomma in på egenvärden och egenvektorer redan efter enförhållandevis kort kurs i linjär algebra. Vid urvalet av stoff har det tagits hänsyn till att vissa studenter kommer att välja att läsa mer linjär algebra efter denna kurs, medan andra inte kommer att göra det.

Denna upplaga har kompletterats med nya avsnitt om bland annat minsta kvadratmetoden och ett stort antal övningar. Gamla tentamensuppgifter förekommer bland dessa. Videoinspelningar av undervisning som ansluter sig till delar av bokens texter och övningar existerar.

Place, publisher, year, edition, pages
Lund: Studentlitteratur AB, 2017. p. 236 Edition: 3
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-64018 (URN)978-91-44-11535-1 (ISBN)
Available from: 2017-05-19 Created: 2017-05-19 Last updated: 2017-10-19Bibliographically approved
Lindström, T. (2017). Monotone dynamics or not?: Dynamical consequences of various mechanisms for delayed logistic growth. Differential Equations & Applications, 9(3), 379-382
Open this publication in new window or tab >>Monotone dynamics or not?: Dynamical consequences of various mechanisms for delayed logistic growth
2017 (English)In: Differential Equations & Applications, ISSN 1847-120X, Vol. 9, no 3, p. 379-382Article in journal (Refereed) Published
Abstract [en]

In this paper we interpret the global stability properties of the delayed single species chemostat in terms of monotone dynamics on an asymptotically invariant hyperplane in the state space. The consequence is a translation of advanced analysis and delay differential equations into sign checks and ordinary differential equations for an important single species model with explicit resource dynamics. Complete proofs are included, since the limiting behavior at asymptotically invariant sets may not agree with the limiting behavior of the original system even in the finite dimensional case (Thieme (1992)). A delayed logistic equation based on explicit resource dynamics falls out as a limiting case of the chemostat and we claim this to be a new mechanistic interpretation of delayed logistic models. We continue by comparing these results to several other delayed logistic models that has been mechanistically justified in the literature. We conclude that monotone dynamics apply in several cases. We improve one global stability result that cannot be obtained with by the use of monotone dynamics and end up by pointing out the dynamical differences between Hutchinson’s (1948) delayed logistic equation and those with mechanistic interpretations.

National Category
Other Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-68272 (URN)10.7153/dea-2017-09-27 (DOI)000416532900006 ()
Available from: 2017-10-09 Created: 2017-10-09 Last updated: 2018-12-12Bibliographically approved
Lindström, T. (2017). Problems in relating various tasks and their samplesolutions to Bloom’s taxonomy. The Montana Mathematics Enthusiast, 14(1-3), 15-28
Open this publication in new window or tab >>Problems in relating various tasks and their samplesolutions to Bloom’s taxonomy
2017 (English)In: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 14, no 1-3, p. 15-28Article in journal (Refereed) Published
Abstract [en]

In this paper we analyze sample solutions of a number of problems and relate them to their level as prescribed by Bloom’s taxonomy. We relate these solutions to a number of other frameworks, too. Our key message is that it remains insufficient to analyze written forms of these tasks. We emphasize careful observations of how different students approach a solution before finally assessing the level of tasks used. We take the arithmetic series as our starting point and point out that the objective of the discussion of the examples here in no way is to indicate an optimal way towards a solution. Instead, our intent is to demonstrate the potential of well selected tasks and the variation that could be observed as students develop their solutions. A large part of this work is devoted to an analysis of the richness of the square triangular number problem.

Place, publisher, year, edition, pages
University of Montana, 2017
Keywords
Bloom’s taxonomy, P´olya problem solving, square triangular numbers, Diophantine problems, continued fractions.
National Category
Other Mathematics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-60069 (URN)000396454000003 ()2-s2.0-85011304760 (Scopus ID)
Available from: 2017-01-23 Created: 2017-01-23 Last updated: 2019-05-28Bibliographically approved
Lindström, T. & Cheng, Y. (2016). A Rosenzweig-MacArthur (1963) Criterion for the Chemostat. Scientific World Journal, Article ID 5626980.
Open this publication in new window or tab >>A Rosenzweig-MacArthur (1963) Criterion for the Chemostat
2016 (English)In: Scientific World Journal, ISSN 1537-744X, E-ISSN 1537-744X, article id 5626980Article in journal (Refereed) Published
Abstract [en]

The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use the implicit function theorem and implicit derivatives for proving that a similar graphical criterion holds under chemostat conditions, too. 

Keywords
Implicit function theorem, stability of equilibria, predator-prey system
National Category
Mathematical Analysis
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-55439 (URN)10.1155/2016/5626980 (DOI)2-s2.0-84982840906 (Scopus ID)
Available from: 2016-08-15 Created: 2016-08-15 Last updated: 2017-11-28Bibliographically approved
Lindström, T. & Nilsson, M. (2015). Låt eleverna ta eget ansvar. Smålandsposten, Article ID 27 jan.
Open this publication in new window or tab >>Låt eleverna ta eget ansvar
2015 (Swedish)In: Smålandsposten, , p. 1article id 27 janArticle in journal, News item (Other (popular science, discussion, etc.)) Published
Abstract [sv]

Hittills har man från politiskt håll kommit med få förslag som berör annat än rent organisatoriska åtgärder för skolan (mindre klasser, när betyg ska ges, läxor eller inte). Enligt vår mening är det viktigare att diskutera hur betygen sätts och hur läxorna ges skriver Marcus Nilsson, prefekt för Institutionen för matematik och Torsten Lindström, professor i matematik.

Place, publisher, year, edition, pages
Växjö: , 2015. p. 1
Keywords
PISA, TiMMS, evaluation criteria, quality in education system
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-41634 (URN)
Available from: 2015-04-01 Created: 2015-04-01 Last updated: 2015-05-04Bibliographically approved
Lindström, T. & Cheng, Y. (2015). Uniqueness of limit cycles for a limiting case of the chemostat: does it justify the use of logistic growth rates?. Electronic journal on the qualitative theory of differential equations (47), 1-14
Open this publication in new window or tab >>Uniqueness of limit cycles for a limiting case of the chemostat: does it justify the use of logistic growth rates?
2015 (English)In: Electronic journal on the qualitative theory of differential equations, ISSN 1417-3875, E-ISSN 1417-3875, no 47, p. 1-14Article in journal (Refereed) Published
Abstract [en]

On infinitesimally short time intervals various processes contributing to population change tend to operate independently so that we can simply add their contributions (Metz and Diekmann, The dynamics of physiologically structured populations, 1986, p. 3). This is one of the cornerstones for differential equations modeling in general. Complicated models for processes interacting in a complex manner may be built up, and not only in population dynamics. The principle holds as long as the various contributions are taken into account exactly. In this paper we discuss commonly used approximations that may lead to non-removable dependency terms potentially affecting the long run qualitative behavior of the involved equations. We prove that these terms do not produce such effects in the simplest and most interesting biological case, but the general case is left open. Our main result is a rather complete analysis of an important limiting case. Once complete knowledge of the qualitative properties of simple models is obtained, it greatly facilitates further studies of more complex models. A consequence of our analysis is that standard methods can be applied. However, the application of those methods is far from straightforward and require non-trivial estimates in order to make them valid for all values of the parameters. We focus on making these proofs as elementary as possible.

Keywords
global stability, uniqueness of limit cycles, chemostat model
National Category
Mathematical Analysis
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-45826 (URN)10.14232/ejqtde.2015.1.47 (DOI)000358722000001 ()2-s2.0-84938592134 (Scopus ID)
Note

I ArXiv med titeln "Logistic approximations and their consequences to bifurcations patterns and long-run dynamics"

Available from: 2015-08-21 Created: 2015-08-21 Last updated: 2017-12-04Bibliographically approved
Lindström, T. (2014). Med Fokus på Linjär Algebra (2ed.). Lund: Studentlitteratur AB
Open this publication in new window or tab >>Med Fokus på Linjär Algebra
2014 (Swedish)Book (Other academic)
Abstract [sv]

Den linjära algebran innehåller i dag ett rikt spektrum av metoder som används och en förståelse för dessa metoder krävs inom nästan alla samhällsområden som använder datorer, beräkningar, bildbehandling eller liknande. Även om verkligheten ofta är icke-linjär, så kräver icke-linjär analys ofta mycket god förståelse av de linjära specialfallen. Få delområden i matematiken kan på en lika elementär nivå klargöra skillnaderna mellan effektiva och mindre effektiva algoritmer och åskådliggöra vilken potential mate­ma­tiken ger för en fortsatt samhällsutveckling.Denna bok riktar sig till den grupp av studenter, som behöver komma in på egenvärden och egenvektorer redan efter en för­hållandevis kort kurs i linjär algebra. Vid urvalet av stoff har det tagits hänsyn till att vissa studenter kommer att välja att läsa mer linjär algebra efter denna kurs, medan andra inte kommer att göra det.Denna upplaga har kompletterats bland annat med ett stort antal övningar. Gamla tentamensuppgifter förekommer bland dessa. Videoinspelningar av undervisning som ansluter sig till delar av bokens texter och övningar existerar.

Place, publisher, year, edition, pages
Lund: Studentlitteratur AB, 2014. p. 206 Edition: 2
Keywords
Linear Algebra, Vector, Gaussian elimination, Matrix, Eigenvalues and Eigenvectors, Linjär Algebra, Vektor, Gausselimnation, Matris, Egenvärden, Egenvektorer
National Category
Mathematics Algebra and Logic
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-36879 (URN)9144093543 (ISBN)9789144093543 (ISBN)
Available from: 2014-09-11 Created: 2014-09-11 Last updated: 2017-01-24Bibliographically approved
Lindström, T. (2013). Dynamical properties of maps fitted to data in the noise-free limit. Paper presented at Selected Papers from the Conference on Innovative Mathematical Methods and Models of Bioscience held in Trento, Italy, in honour of Mimmo Iannelli. Journal of Biological Dynamics, 7(S1), 108-116
Open this publication in new window or tab >>Dynamical properties of maps fitted to data in the noise-free limit
2013 (English)In: Journal of Biological Dynamics, ISSN 1751-3758, E-ISSN 1751-3766, Vol. 7, no S1, p. 108-116Article in journal (Refereed) Published
Abstract [en]

We argue that any attempt to classify dynamical properties from nonlinear finite time-series data requires a mechanistic model fitting the data better than piecewise linear models according to standard model selection criteria. Such a procedure seems necessary but still not sufficient.

Place, publisher, year, edition, pages
Taylor & Francis, 2013
Keywords
deterministic chaos, model selection, regression model, time-series, threshold autoregressive model, skew tent map, uniqueness of periodic attractors, difference equation, bifurcation diagram
National Category
Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-30517 (URN)10.1080/17513758.2013.804127 (DOI)000341270500008 ()2-s2.0-84888133723 (Scopus ID)
Conference
Selected Papers from the Conference on Innovative Mathematical Methods and Models of Bioscience held in Trento, Italy, in honour of Mimmo Iannelli
Available from: 2013-11-19 Created: 2013-11-19 Last updated: 2017-12-06Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-7261-0399

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