Nonlinear and Biomedical Physics at Lancaster University

We are studying 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. The time-variability is inherent, on account of the system's ability to adjust its characteristic frequencies and adopt 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 fully deterministic. We are now developing methods for inferring the dynamics of chronotaxic systems from real data.

By applying ideas and methods from nonlinear and stochastic dynamics we study fundamental physical properties of living systems. On the nanoscale, we study 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, i.e. the conundrum 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 for patients in our collaborating hospitals is illuminating and characterising diverse conditions and diseases.

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 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