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The transition of a counter chemotactic particle flow from a free-flow stateto a jammed state in a quasi-one-dimensional path is investigated. One of thecharacteristic features of such a flow is that the constituent particlesspontaneously form a cluster that blocks the path, called a path-blockingcluster (PBC), and causes a jammed state when the particle density is greaterthan a threshold value. Near the threshold value, the PBC occasionally desolveitself to recover the free flow. In other words, the time evolution of the sizeof the PBC governs the flux of a counter chemotactic flow. In this paper, onthe basis of numerical results of a stochastic cellular automata (SCA) model,we introduce a Langevin equation model for the size evolution of the PBC thatreproduces the qualitative characteristics of the SCA model. The resultssuggest that the emergence of the jammed state in a quasi-one-dimensionalcounter flow is caused by a saddle-node bifurcation.

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