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Simulation and Mathematical Analysis of a Task Partitioning Model of a Colony of Ants
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
2016 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

In this thesis we study a mathematical model that describes task partitioning in a colony of ants. This process of self-organization is modeled by a nonlinear coupled system of rst order autonomous ordinary dierential equations. We discuss how this system of equations can be derived based on the behavior of ants in a colony. We use GNU Octave (a high-level programming language) to solve the system of equations numerically for dierent sets of parameters and show how the solutions respond to changes in the parameter values.

Finally, we prove that the model is well-posed locally in time. We rewrite the system of ordinary dierential equations in terms of a system of coupled Volterra integral equations and look at the right-hand side of the system as a nonlinear operator on a Banach space. By doing so, we have transformed the problem of showing existence and uniqueness of solutions to a system of ordinary dierential equations into a problem of showing existence and uniqueness of a xed point to the corresponding integral operator. Additionally, we use Gronwall's inequality to prove the stability of solutions with respect to data and parameters.

Place, publisher, year, edition, pages
2016. , p. 65
Keywords [en]
Social insects, Ants, Task partitioning, Self-organization, Nonlinear operators, Dynamical systems, Fixed point theorems
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-70161OAI: oai:DiVA.org:kau-70161DiVA, id: diva2:1263952
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Available from: 2018-11-20 Created: 2018-11-18 Last updated: 2018-11-20Bibliographically approved

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