On discrete and continuous state adaptive network models

On discrete and continuous state adaptive network models: with an application to self-organisation in swarming systems

van de Kamp, Carsten T. (TU Delft Applied Sciences; TU Delft Electrical Engineering, Mathematics and Computer Science)

Idema, Timon (mentor)
Dubbeldam, Johan (mentor)
Thijssen, Jos (graduation committee)
Nane, Tina (graduation committee)

Delft University of Technology

Applied Mathematics | Applied Physics

2019-07-14

We consider adaptive network models with discrete and continuous state sets obeying dynamical rules that enable application to swarming systems. The 2-state adaptive network contains a supercritical pitchfork bifurcation in the transition between ordered and disordered stationary solutions. We derive an adaptive network model that works on a continuous state set and apply it to swarming motion in both a mean field and a moment closure approximation. In numerical solutions of the mean field approximation the relation between the variance of the ordered stationary distributions and the system parameters is given by a square root function. Cauchy distributions form a good fit to these steady state distributions, although they are not the analytic stationary solutions. We show that in numerical solutions of the moment closure approximation a bistable region is formed, in which the initial condition determines if the system ends up in an ordered or a disordered state. Further research could focus on finding the exact details of the corresponding subcritical pitchfork and saddle-node bifurcations and comparing the derived models to real-life swarming systems.

Adaptive Networks
Differential Equations
Modelling
Bifurcation Analysis
Partial Differential Equations
Complex Networks
Complex Adaptive Systems
Swarming
Self-organisation
Collective motion

http://resolver.tudelft.nl/uuid:9b4b4396-4288-4c89-b8a4-1e52c75d83bc

Student theses

bachelor thesis

© 2019 Carsten T. van de Kamp