# Berlin 2008 – wissenschaftliches Programm

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# SYDN: Symposium Game theory in dynamical systems

## SYDN 1: Game theory in dynamical systems

### SYDN 1.6: Vortrag

### Freitag, 29. Februar 2008, 11:50–12:05, H 0105

**Discrete stochastic dynamics in dynamical systems with limit cycles** — •Richard Boland, Tobias Galla, and Alan McKane — The University of Manchester

Chemical systems are often described by a set of reaction equations between discrete numbers of particles. Similarly, models in population dynamics can be formulated on the level of individuals, who may reproduce or feed upon each other. In the limit of infinite system size a continuous mean-field description can be derived in terms of a set of ordinary differential equations for the concentrations of different chemicals or species. Stochastic effects in systems with finite size have recently been shown to be relevant in, for example, prey-predator systems, where the mean field theory predicts a stable fixed point and no persistent oscillations. At finite size, however, systems can show coherent oscillations via a resonant amplification of inherent noise due to discretisation. In this talk we focus on systems where the attractor of the mean field-dynamics is a limit cycle (e.g. the Brusselator), and address finite-size stochastic effects by means of an expansion of the master equation in the inverse system size, resulting in a stochastic Langevin equation for the fluctuations about the limit cycle. We demonstrate how analytical progress can be made in a co-moving frame, and compute the power spectra of the transverse and longitudinal components.