Dynamical Systems

Dynamical systems theory studies how systems evolve under differential equations, focusing on trajectories, fixed points, stability under linearisation, and bifurcations where qualitative behaviour changes. Classical tools include Lyapunov functions, invariant manifolds, and geometric structures that determine long-term behaviour. Compartmental models in pharmacology are low-dimensional dynamical systems; their fixed points represent steady state concentrations, their linearisations reveal how perturbations decay, and their GENERIC structure encodes the dissipative geometry underlying reversible and irreversible processes.