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Interacting particle systems in biology, chemistry and the social sciences are traditionally described by ordinary or partial differential equations. These are purely deterministic and based on the assumption that effects of noise can safely be neglected. Such approaches are no doubt chosen for their mathematical simplicity, the theory of differential equations is well developed, whereas existing theories of non-equilibrium stochastic dynamics are more complex and largely incomplete. In this talk I will consider systems of a finite number of interacting particles, their intrinsic stochasticity can then no longer be ignored. I will discuss noise-induced phenomena such as quasi-cyles, quasi-Turing patterns and travelling quasi waves, and explain how they can be characterised analytically within the so-called linear noise approximation. Examples where this is relevant include systems in evolutionary dynamics, game theory and chemical reaction systems. One focus of the talk will be on models with delay dynamics, important for example in gene regulatory systems or in epidemiology. I will show how path-integral approaches can be used to derive general results for their chemical Langevin equation and linear-noise approximation.

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Dr. Tobias Galla, University of Manchester
Seminarraum Theoretische Physik
Contact: not specified