Chemotactic predator-prey dynamics

TL;DR

This paper introduces a discrete chemotactic predator-prey model where prey and predator secrete chemicals sensed by each other, revealing unstable steady states and complex diffusive behaviors that help classify bacterial and immune cell motility.

Contribution

It presents a novel discrete chemotactic predator-prey model with analysis of dynamical states and transient behaviors, advancing understanding of microbial and immune cell interactions.

Findings

Steady hunting is unstable in the model.

Escape dynamics show transient subdiffusive behavior with a $t^{1/3}$ scaling.

Certain parameter regions correspond to infallible predators.

Abstract

A discrete chemotactic predator-prey model is proposed in which the prey secrets a diffusing chemical which is sensed by the predator and vice versa. Two dynamical states corresponding to catching and escaping are identified and it is shown that steady hunting is unstable. For the escape process, the predator-prey distance is diffusive for short times but exhibits a transient subdiffusive behavior which scales as a power law $t^{1/3}$ with time $t$ and ultimately crosses over to diffusion again. This allows to classify the motility and dynamics of various predatory bacteria and phagocytes. In particular, there is a distinct region in the parameter space where they prove to be infallible predators.