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#### Open Access in DiVA

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#### Authority records

Gyllingberg, Linnéa
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Department of Mathematics
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The Art of Modelling Oscillations and Feedback across Biological ScalesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2024 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Description

##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Department of Mathematics, 2024. , p. 48
##### Series

Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 135
##### Keywords [en]

mathematical biology, mathematical modelling, oscillations, feedback mechanisms, dynamical systems, individual-based models, complex systems
##### National Category

Mathematics
##### Research subject

Applied Mathematics and Statistics
##### Identifiers

URN: urn:nbn:se:uu:diva-523639ISBN: 978-91-506-3039-8 (print)OAI: oai:DiVA.org:uu-523639DiVA, id: diva2:1839681
##### Public defence

2024-04-12, Sonja Lyttkens (101121), Ångströmlaboratoriet, Uppsala, 09:15 (English)
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt689",{id:"formSmash:j_idt689",widgetVar:"widget_formSmash_j_idt689",multiple:true}); Available from: 2024-03-19 Created: 2024-02-21 Last updated: 2024-03-19
##### List of papers

This thesis consists of four papers in the field of mathematical biology. All papers aim to advance our understanding of biological systems through the development and application of innovative mathematical models. These models cover a diverse range of biological scales, from the nuclei of unicellular organisms to the collective behaviours of animal populations, showcasing the broad applicability and potential of mathematical approaches in biology. While the first three papers study mathematical models of very different applications and at various scales, all models contribute to the understanding of how oscillations and/or feedback mechanisms on the individual level give rise to complex emergent patterns on the collective level. In Paper I, we propose a mathematical model of basal cognition, inspired by the true slime mould, *Physarum polycephalum.* The model demonstrates how a combination of oscillatory and current-based reinforcement processes can be used to couple resources in an efficient manner. In Paper II, we propose a model of social burst-and-glide motion in pairs of swimming fish by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. Our model, in which visual stimuli of the position of the other fish affect the internal burst or glide state of the fish, captures a rich set of swimming dynamics found in many species of fish. In Paper III, we study a class of spatially explicit individual-based models with contest competition. Based on measures of the spatial statistics, we develop two new approximate descriptions of the spatial population dynamics. Paper IV takes a reflective turn, advocating from a philosophical perspective the importance of developing new mathematical models in the face of current scientific challenges.

1. A minimal model of cognition based on oscillatory and reinforcement processes$(function(){PrimeFaces.cw("OverlayPanel","overlay1838668",{id:"formSmash:j_idt745:0:j_idt751",widgetVar:"overlay1838668",target:"formSmash:j_idt745:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Using neuronal models to capture burst-and-glide motion and leadership in fish$(function(){PrimeFaces.cw("OverlayPanel","overlay1787107",{id:"formSmash:j_idt745:1:j_idt751",widgetVar:"overlay1787107",target:"formSmash:j_idt745:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Finding analytical approximations for discrete, stochastic, individual-based models of ecology$(function(){PrimeFaces.cw("OverlayPanel","overlay1600612",{id:"formSmash:j_idt745:2:j_idt751",widgetVar:"overlay1600612",target:"formSmash:j_idt745:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. The lost art of mathematical modelling$(function(){PrimeFaces.cw("OverlayPanel","overlay1790555",{id:"formSmash:j_idt745:3:j_idt751",widgetVar:"overlay1790555",target:"formSmash:j_idt745:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

isbn
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