Spatio-temporal Dynamics of the Haken Lighthouse Model

Project description

 

The Lighthouse Model, introduced by Hermann Haken — the founder of synergetics — was designed to bridge the gap between detailed spiking neural network models and simplified rate- or phase-based descriptions of brain activity. This model exhibits remarkably rich spatio-temporal dynamics that are deeply relevant to modern theoretical neuroscience but remain only partially understood from a mathematical standpoint. This project will apply and extend methods from applied nonlinear dynamical systems theory to uncover new insights into synchronisation, travelling waves, and pattern formation in Lighthouse networks. These networks will be studied on graph structures incorporating realistic synaptic interactions (modelled by alpha-function synapses) and plastic axonal conduction delays, capturing biologically plausible mechanisms of neural communication. The work will integrate analytical tools from mathematical biology (such as Turing instability analysis) and network science (including graph-theoretic and computational approaches) with techniques from non-smooth dynamical systems (e.g., saltation operators). Through this synthesis, the project aims to develop a comprehensive understanding of how waves, bumps, and complex spatio-temporal patterns self-organise in Lighthouse networks, advancing the synergetic framework and deepening our theoretical grasp of neural dynamics.