Module description
Syllabus
Stochastic processes; Markov processes, Master equation, Markov Chains and One step processes; Steady state, time reversibility and Detailed balance; Fokker-Planck equation, Boltzmann equilibrium as steady state; Langevin equation, Kramers-Moyal coefficients; Linear response and fluctuation-dissipation theorem; Macroscopic analysis of dynamics; Path integral formalism; Simple dynamical processes on complex networks; Applications to complex and disordered systems.
Prerequisites:
A good knowledge of multivariate calculus and linear algebra and a background of ordinary and partial differential equations and probability theory is required.
Assessment details
2 hour written examination.
Educational aims & objectives
Aims
(i) Gain an understanding of dynamical analysis of complex systems and familiarize with the tools to work with research-based knowledge at the forefront of this field
(ii) Demonstrate some applications of the techniques and methodology to complex systems modelling in mathematics and other disciplines.
Teaching pattern
Two hours of lectures and one hour of tutorial per week throughout the term
Suggested reading list
Indicative reading list - link to Leganto system where you can search with module code for lists