Dynamical phenomena induced by bottleneck

Dynamical phenomena induced by bottleneck.

We study a microscopic follow-the-leader model on a circle of length L with a bottleneck. Allowing large bottleneck strengths we encounter very interesting traffic dynamics. Different types of waves--travelling and standing waves and combinations of both wave types--are observed. The way to find these phenomena requires a good understanding of the complex dynamics of the underlying (nonlinear) ...

Weak-noise-induced phenomena in a slow-fast dynamical system

This thesis considers a stochastic dynamical system that has multiple time scales. The focus lies on the planar slow-fast stochastic differential equation (a singularly perturbed stochastic system) modeling the spiking activity of an isolated FitzHugh-Nagumo neural oscillator. We analyze the model equation on the slow time scale τ (Eq.(1)) and on the fast time scale t (Eq.(2)). { dvτ = ε f(vτ ,...

Past-future information bottleneck in dynamical systems.

Biological systems need to process information in real time and must trade off accuracy of presentation and coding costs. Here we operationalize this trade-off and develop an information-theoretic framework that selectively extracts information of the input past that is predictive about the output future, obtaining a generalized eigenvalue problem. Thereby, we unravel the input history in terms...

Coherent Phenomena in Stochastic Dynamical Systems

The paper develops the basic ideas of statistical topography of random processes and ̄elds to analyze coherent phenomena in simple dynamical systems. Such phenomena take place with probability one, and provide links between individual realizations and statistical characteristics of system at large. We con ̄ne ourselves to several examples: the transfer phenomena in singular dynamic systems under...

Dynamical modeling with application to friction phenomena