Time-varying sync

sync with time-varying parameters

Synchronisation is a well-known phenomenon that plays a key role in physics, biology, and neuroscience, to cite a few. A typical example is when people in an audience clap in unison, because of their (audio and visual) interactions, or when heart cells synchronise to make the heart beat. A lot of theoretical work exists on synchronisation, but mostly considers the frequencies of each unit to be constant. In nature, and in living systems in particular, however, frequencies change all the time. Imagine how our heartbeat changes when we are calm, stressed, or scared.

This is what motivates our studies on synchronisation between oscillators with time-varying parameters. In particular, in different studies, we consider time-varying frequencies, coupling strenghts, and network structure.

More formally, an example system we considered is the following: a network driven by an oscillator with a time-varying frequency,

\[\dot \theta_i = \omega + D \sum_{j=1}^N A_{ij} \sin(\theta_j - \theta_i) + \gamma \sin(\theta_i - \theta_0(t)) ,\]

which we analysed by doing performing a linear stability analysis, among other things.

This was my PhD project, and you can find more information about it in the references below.


Journal articles
  1. Stabilization of cyclic processes by slowly varying forcing
    J. Newman,  M. Lucas, and  A. Stefanovska
    Chaos, 2021
  2. Nonautonomous driving induces stability in network of identical oscillators
    M. Lucas,  D. Fanelli, and  A. Stefanovska
    Phys. Rev. E, 2019
  3. Desynchronization induced by time-varying network
    M. Lucas,  D. Fanelli,  T. Carletti, and  J. Petit
    Europhys. Lett., 2018
  4. Stabilization of dynamics of oscillatory systems by nonautonomous perturbation
    M. Lucas,  J. Newman, and  A. Stefanovska
    Phys. Rev. E, 2018
Book chapters
  1. Synchronisation and Non-autonomicity
    M. Lucas,  J. Newman, and  A. Stefanovska
    In Physics of Biological Oscillators, 2021
  2. Non-asymptotic-time Dynamics
    J. Newman,  M. Lucas, and  A. Stefanovska
    In Physics of Biological Oscillators, 2021
PhD thesis
  1. Synchronisation and stability in nonautonomous oscillatory systems
    M. Lucas
    Lancaster University and University of Florence, 2019