Pulsed interaction signals as a route to biological pattern formation

TL;DR

This paper introduces a mechanism for biological pattern formation driven by pulsed interaction signals, demonstrating how signal speed influences the emergence of spatial patterns and connecting reaction-diffusion and nonlocal models.

Contribution

It presents a unified population-signal framework showing how pulsed signals can induce pattern formation, linking reaction-diffusion and nonlocal models in biological systems.

Findings

Fast pulsed signals enable pattern formation.

Slow signals do not produce patterns.

The framework bridges reaction-diffusion and nonlocal models.

Abstract

We identify a mechanism for biological spatial pattern formation arising when the signals that mediate interactions between individuals in a population have pulsed character. Our general population-signal framework shows that while for a slow signal-dynamics limit no pattern formation is observed for any values of the model parameters, for a fast limit, on the contrary, pattern formation can occur. Furthermore, at these limits, our framework reduces, respectively, to reaction-diffusion and spatially nonlocal models, thus bridging these approaches.