Saddle-Node Bifurcation to Jammed State for Quasi-One-Dimensional Counter Chemotactic Flow

TL;DR

This paper investigates the transition from free flow to jammed state in counter chemotactic particle flow, identifying a saddle-node bifurcation as the underlying mechanism through a Langevin equation model.

Contribution

It introduces a Langevin equation model for the path-blocking cluster dynamics, revealing the bifurcation causes of jamming in counter chemotactic flow.

Findings

Jamming occurs via a saddle-node bifurcation.

The Langevin model reproduces key features of the cellular automata simulations.

PBC size dynamics govern flow transitions.

Abstract

The transition of a counter chemotactic particle flow from a free-flow state to a jammed state in a quasi-one-dimensional path is investigated. One of the characteristic features of such a flow is that the constituent particles spontaneously form a cluster that blocks the path, called a path-blocking cluster (PBC), and causes a jammed state when the particle density is greater than a threshold value. Near the threshold value, the PBC occasionally desolve itself to recover the free flow. In other words, the time evolution of the size of the PBC governs the flux of a counter chemotactic flow. In this paper, on the basis of numerical results of a stochastic cellular automata (SCA) model, we introduce a Langevin equation model for the size evolution of the PBC that reproduces the qualitative characteristics of the SCA model. The results suggest that the emergence of the jammed state in a quasi-one-dimensional counter flow is caused by a saddle-node bifurcation.