The Principle of Linearized Stability in Age-Structured Diffusive Populations

TL;DR

This paper proves the principle of linearized stability for age-structured diffusive populations with nonlinear birth and death processes, showing exponential stability under certain spectral conditions.

Contribution

It establishes a general abstract framework for stability analysis and applies it to specific models of age-structured populations with diffusion.

Findings

Exponential stability is achieved for equilibria with a negative growth bound.

The stability principle is valid for nonlinear birth and death processes.

The results are applicable to concrete biological population models.

Abstract

The principle of linearized stability is established for age-structured diffusive populations incorporating nonlinear death and birth processes. More precisely, asymptotic exponential stability is shown for equilibria for which the semigroup associated with the linearization at the equiblibrium has a negative growth bound. The result is derived in an abstract framework and applied in concrete situations.