Hopf Bifurcation in Structural Population Models

TL;DR

This paper rigorously demonstrates the existence of Hopf bifurcations in a nonlinear PDE model inspired by myxobacteria, establishing the presence of periodic solutions related to cell density wave patterns.

Contribution

It provides a rigorous mathematical proof of Hopf bifurcations in a PDE model, revealing conditions for periodic solutions in biological pattern formation.

Findings

Existence of Hopf bifurcations for specific parameter values

Periodic solutions in the PDE model

Connection to biological cell density waves

Abstract

We study a nonlinear PDE problem motivated by the peculiar patterns arising in myxobacteria, namely counter-migrating cell density waves. We rigorously prove the existence of Hopf bifurcations for some specific values of the parameters of the system. This shows the existence of periodic solutions for the systems under consideration.