Complex Dynamics in Spatially Extended Systems

Stochastic population dynamics in spatially extended predator-prey systems

Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting manyparticle systems beyond rate equation approximations. Including spatial structure ...

Dynamics of Spatially Extended Dendrites

Dendrites are the most visually striking parts of neurons. Even somany neuron models are of point type and have no representation of space. In this thesis we will look at a range of neuronal models with the common property that we always include spatially extended dendrites. First we generalise Abbott’s “sumover-trips” framework to include resonant currents. We also look at piece-wise linear (P...

Transient dynamics and nonlinear stability of spatially extended systems.

As studies of various systems have shown, the sole focus on the eigenvalues in a linear stability analysis can be misleading, especially when the dynamics of disturbances is characterized by strong transient growth. The aim of this paper is to extend the generalized stability analysis, in the context of spatially extended systems, by examining the role of the nonlinear terms in the destabilizat...

Entropy Production in Driven Spatially Extended Systems

This is a short review of the statistical mechanical definition of entropy production for systems composed of a large number of interacting components. Emphasis is on open systems driven away from equilibrium where the entropy production can be identified with a logarithmic ratio of microstate multiplicities of the original macrostate with respect to the time-reversed state. A special role is t...

Finite Propagation Speeds in Spatially Extended Systems