January 24, 2024
Abstract: By designing coupling to control populations of oscillators, we can control their synchonisation behaviour. Oscillators (e.g. neurons) can be coupled on different levels. The most basic level is through links between pairs of oscillators. However, using graphs with only pairwise links is not necessarily a satisfactory approximation of reality as nonpairwise interactions can be found in many dynamical systems including social networks and the human brain. Even though the effects of these nonpairwise interactions have been observed, described and modeled in a wide range of oscillatory systems, controlling nonpairwise interactions in arbitrary populations of oscillators has remained a relatively unexplored area. In this thesis we generalise synchronisation engineering to control nonpairwise interactions in arbitrary systems. We designed a nonlinear time-delayed coupling that can be used to match the phase reduction of a system of oscillators to a target phase model. The contribution of this thesis is allowing for nonpairwise interactions in the target phase model. We used an optimisation proceidure to find coupling parameters to match a nonpairwise target phase model that has the collective behaviour we aim to introduce to the system We found that we need one additional filter to find the parameter sets that match the bifurcation of both in-phase and splay configuration in to the nonpairwise target phase model.
June 14, 2022
An outreach article for Videnskab.dk, find it here (in Danish).
May 27, 2021
Abstract: By designing feedback to control populations of oscillators, synchronisation in neurons causing epileptic seizures can be broken up. Oscillators (e.g. neurons) can be coupled on different levels. The most basic level is through links between pairs of oscillators. These pairwise links fail to explain phenomena such as peer pressure. The nonpairwise ‘links’ make such phenomena possible. Even though the effects of these nonpairwise interactions have been observed, described and modelled in a wide range of oscillatory systems, controlling nonpairwise interactions in arbitrary systems has remained a mainly unexplored area. We generalize synchronisation engineering to control nonpairwise interactions in arbitrary systems. As a first step, we design nonlinear time-delayed feedback that introduces bifurcations away from splay configuration into arbitrary systems. Controlling nonpairwise interactions might advance the design of minimum-power stimuli for the treatment of epilepsy.
February 25, 2021
Abstract: We will go through the concepts of oscillators, phase, isochrones, phase response curves and phase reduction. We then use phase reduction techniques to design weak nonlinear time-delayed feedback to control arbitrary oscillatory systems. The collective behaviour that we introduce to a system of oscillators in this way is described by a target phase model. In our generalisation of this (“synchronisation engineering”) approach, the target phase model can have nonpairwise interactions. Controlling nonpairwise interactions might advance the design of minimum-power stimuli for the treatment of epilepsy.
August 27, 2020
Abstract: By designing feedback to control populations of oscillators, synchronisation in neurons causing epileptic seizures can be broken up. Oscillators (e.g. neurons) can be coupled on different levels. The most basic level is through links between pairs of oscillators. These pairwise links fail to explain phenomena such as peer pressure. The nonpairwise ‘links’ make such phenomena possible. Even though the effects of these nonpairwise interactions have been observed, described and modeled in a wide range of oscillatory systems, controlling nonpairwise interactions in arbitrary systems has remained a mainly unexplored area. We generalize synchronisation engineering to control nonpairwise interactions in arbitrary systems. As a first step, we design nonlinear time- delayed feedback that introduces bifurcations away from splay configuration into arbitrary systems. Controlling nonpairwise interactions might advance the design of minimum-power stimuli for the treatment of epilepsy.
June 19, 2020
Talk at the International Women in Engineering Day (INWED) at the University of Exeter.
April 9, 2020
Talk at the Dynamics Internal Seminar at the University of Exeter.
March 28, 2019
Talk at the Dynamics Internal Seminar at the University of Exeter. See Chapter 2 of my master thesis.
June 1, 2018
Abstract: Fænomenet synkronisering er blevet undersøgt ved hjælp af Kuramoto modellen samt med forskellige tilpasninger deraf. Denne model beskriver en stor population af koblede oscillatorer. Tilpasningerne som er undersøgt her inkluderer en bimodal frekvens fordeling, tilføjelse af hvid støj, kobling afhængig af beliggenhed og en uniform faseforskydning. Vi reproducerer analyser og udfører simulationer, hvor blandt andet Monte Carlo metoder er brugt. Ved hjælp af tid-frekvens analyse baseret på wavelets er vi i stand til at opdage partiel synkronisering.
June 1, 2016
Abstract: The phenomenon of synchronisation is studied by means of the Kuramoto model. This model describes a large population of coupled oscillators with natural frequencies taken from a narrow distribution. It is assumed that the coupling between the oscillators is mean-field and purely sinusoidal. We follow Kuramoto’s analysis to obtain a formula for the critical coupling. Then the properties of the Kuramoto model are studied with the aid of Poincaré maps. We then conclude with a time-frequency analysis of the order parameter. With the aid of this time-frequency analysis we were able to detect partial synchronisation.