A man lies on a bed whilst a student monitors aspects of his health

Nonlinear and Biomedical Physics

Research Areas

We study oscillatory dynamics, theoretically, numerically and from measured data. We have pioneered the understanding of a living system as a collection of time-varying oscillatory processes.

Time-variability is inherent, on account of the system's ability to adjust its characteristic frequencies and adapt to changing circumstances. We have introduced a new class of systems and named them chronotaxic systems (from Chronos - time, and taxis - order). Chronotaxic systems are non-autonomous self-sustained oscillators that possess point attractor. They provide a route to stability in highly complex systems. Until now, such systems have mostly been treated as stochastic, whereas we have recently shown that they can be entirely deterministic. We are currently developing methods for inferring the dynamics of chronotaxic systems from real data.

By applying ideas and methods from nonlinear and stochastic dynamics, we study the fundamental physical properties of living systems. On the nanoscale, we examine ion channels. We treat the permeation of ion channels as a problem in stochastic nonlinear dynamics and electrostatics, illuminating the long-standing conduction-selectivity paradox. That is to say, the issue of how channels can be highly selective for particular species of ion, yet still conduct at an enormous rate, almost as though they were just open holes in the cell membrane.

Oscillations are a universal phenomenon in living systems. We investigate oscillatory behaviour on all scales and levels of complexity - from the cell membrane potential to cardiovascular and brain dynamics. We are especially interested in the influence of the oscillators on each other - their mutual interactions and coupling functions. The resultant modulation and synchronisation phenomena occur in physiology in just the same way that they do for coupled oscillators in physics. Comparison of the model phenomena with physiological data measured for healthy subjects in our laboratory and patients in our collaborating hospitals is illuminating and characterising diverse conditions and diseases.


We also develop software toolboxes to investigate these phenomena.

Key Research

  • Chronotaxic systems - theory and methods for data analyses
  • Networks of oscillators
  • Time-varying Kuramoto model of phase oscillators
  • Analysis of time-varying dynamics
  • Bayesian inference for time-varying systems
  • Nonlinear mode decomposition
  • Ion channels
  • Oscillations in cell membrane potential
  • Applications
  • Cancer as a state of decoupled oscillators at the endothelial level
  • Hypertension and phase coherence between cardiovascular oscillators
  • Cardiovascular and brain dynamics in anaesthesia
  • Cardio-respiratory coupling function as a marker of ageing
  • Spatio-temporal brain dynamics in autism

For full information on the work of the Nonlinear and Biomedical Physics research group, follow this link to access our research portal.

Nonlinear and Biomedical Physics

Current PhD Opportunities


Postgraduate Training

The Nonlinear and Biomedical Physics group runs training workshops for postgraduate students throughout the year, covering both subject-specific and more general research skills.

The form and content of the workshops are determined through dialogue with the PhD students so that the most effective training can be provided. Although the events are designed to meet the needs of students in Nonlinear and Biomedical Physics, they are also available to other postgraduate students on request, as well as to MPhys project students working within the group. Additional training is offered by the Faculty of Science and Technology, ISS, and the Library.

Our students attend a variety of scientific conferences, for which they receive support in the preparation of posters and oral presentations. They also have the opportunity to develop their presentation skills via participation in the Department’s outreach programme. They play an important role in working with the A-level and internship students that visit our group during the summer.

Recent tutorials, workshops and conferences include:

  • Nonlinear time series analysis methods (October 2015) – Professor A. Stefanovska
  • Ionic Coulomb blockade oscillations and the physical origins of permeation, selectivity, and their mutation transformations in biological ion channels (October 2015) – Professor PVE McClintock (chair)
  • Biological Oscillations ESGCO–2016 Conference (10-14 April 2016) [Covered talks on topics including biological ion channels, cellular, cardiovascular and brain dynamics, data analysis methods, theories of coupled oscillators and networks, non-autonomous dynamics] - Professor A. Stefanovska (chair)
  • Reconstructing non-autonomous dynamics (November 2015) – Professor A. Stefanovska
  • Introduction to MatLab and wavelet analysis tutorial November 2015– Dr G. Lancaster
  • Inverse approaches to dynamical systems tutorial February 2016 – Dr G. Lancaster
  • Physics of living systems (February 2016)– Professor A. Stefanovska

Our students are part of two Horizon 2020 Marie Skłodowska-Curie training networks:

  • Complex Oscillatory Systems: Modelling and Analysis (COSMOS): Innovative Training Network – European Joint Doctorate
  • Critical Transitions in Complex Systems (CRITICS)

Students have the possibility of attending summer schools organised by both networks:

  • First COSMOS school and workshop, Florence, Italy, November 2015.
  • Second COSMOS school and workshop, Aberdeen, UK, 27th June - 6th July 2016.
  • Workshop on Critical Transitions in Complex Systems, Copenhagen, Denmark, 4-9 September 2016.

as well as a variety of national and international summer schools relevant to their projects.

Nonlinear and Biomedical Physics Toolboxes

Here you can find GitHub links for the numerical toolbox MODA and algorithms developed by the Nonlinear and Biomedical Physics group at Lancaster University for analysing time-series data, either measured or numerically generated.


MODA is a user-friendly toolbox, written both in MatLab and in Python. It is designed for analysing time-series that result from multiscale oscillatory dynamics. It encompasses non-autonomous dynamics in which frequencies vary in time. MODA provides time-frequency spectra and enables detection of instantaneous frequencies. It includes an algorithm to detect high harmonics of time-varying frequencies.

MODA also contains algorithms for the investigation of interactions between oscillatory processes, including wavelet phase coherence and phase shifts, wavelet bispectral analysis, and coupling functions obtained through dynamical Bayesian inference.

MODA includes methods for univariate and simultaneously recorded/generated multivariate time-series.

Other downloads

These are algorithms and toolboxes that can be run individually. Some of them are included in MODA. They are all written in MatLab.