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A gradient flow approach to the model of positive feedback in decision-making
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2015 (English)In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 77, 215-224 p.Article in journal (Refereed) Published
Abstract [en]

Recent studies on social dynamics have been done by using tools and methods of physics and economics.. The main idea is that the regularity observed on a global scale arises out of local interactions between the group members. We consider the model describing one of the major interaction mechanism, the model of positive feedback. We propose a geometrical reformulation of this model in terms of gradient flow equations on a Riemannian manifold. The benefit of this reformulation is that we introduce an alternative method to study phenomena of the well known model. We suggest the analogy with a particle moving on curved manifold. We believe that this analogy will allow us to extend powerful mathematical tools from analytical mechanics to the biological systems.

Place, publisher, year, edition, pages
2015. Vol. 77, 215-224 p.
Keyword [en]
Mathematical model of positive feedback in decision making, Gradient flow equations, Differential geometry
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-261246DOI: 10.1016/j.chaos.2015.05.027ISI: 000358970500022OAI: oai:DiVA.org:uu-261246DiVA: diva2:851707
Available from: 2015-09-07 Created: 2015-08-31 Last updated: 2017-12-04
In thesis
1. Mathematical modelling approach to collective decision-making
Open this publication in new window or tab >>Mathematical modelling approach to collective decision-making
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In everyday situations individuals make decisions. For example, a tourist usually chooses a crowded or recommended restaurant to have dinner. Perhaps it is an individual decision, but the observed pattern of decision-making is a collective phenomenon. Collective behaviour emerges from the local interactions that give rise to a complex pattern at the group level. In our example, the recommendations or simple copying the choices of others make a crowded restaurant even more crowded. The rules of interaction between individuals are important to study. Such studies should be complemented by biological experiments. Recent studies of collective phenomena in animal groups help us to understand these rules and develop mathematical models of collective behaviour. The most important communication mechanism is positive feedback between group members, which we observe in our example. In this thesis, we use a generic experimentally validated model of positive feedback to study collective decision-making.

The first part of the thesis is based on the modelling of decision-making associated to the selection of feeding sites. This has been extensively studied for ants and slime moulds. The main contribution of our research is to demonstrate how such aspects as "irrationality", speed and quality of decisions can be modelled using differential equations. We study bifurcation phenomena and describe collective patterns above critical values of a bifurcation points in mathematical and biological terms. In the second part, we demonstrate how the primitive unicellular slime mould Physarum Polycephalum provides an easy test-bed for theoretical assumptions and model predictions about decision-making. We study its searching strategies and model decision-making associated to the selection of food options. We also consider the aggregation model to investigate the fractal structure of Physarum Polycephalum plasmodia.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2017. 42 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 99
Keyword
collective behaviour, collective decision-making, communication mechanisms, positive feedback, mathematical modelling, bifurcation phenomena, steady state solutions, symmetry breaking, symmetry restoring, diffusion-limited aggregation, fractal dimension
National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-314903 (URN)978-91-506-2624-7 (ISBN)
Public defence
2017-04-07, Siegbahnsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Note

Fel serie i tryckt bok /Wrong series in the printed book

Available from: 2017-03-16 Created: 2017-02-07 Last updated: 2017-03-16

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Zabzina, Natalia

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