Robust uniform persistence for structured models of delay differential equations

Paul L. Salceanu

doi:10.3934/dcdsb.2021258

Article Contents

2022, Volume 27, Issue 9: 4923-4939. Doi: 10.3934/dcdsb.2021258

This issue Previous Article Global existence of weak solutions to inhomogeneous Doi-Onsager equations Next Article Inverse scattering transform for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation

Robust uniform persistence for structured models of delay differential equations

Paul L. Salceanu

University of Louisiana at Lafayette, Lafayette, LA 70503, USA

Received: March 31, 2021

Revised: July 31, 2021

Early access: November 2021

Published: September 2022

The author is supported by a Simons Foundation Collaboration Grant for Mathematicians. Award ID: 524761

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Abstract

We consider a general class of delay differential equations systems, typically used to model the dynamics of structured biological populations, and establish necessary conditions for the part of the attractor contained in the boundary of the state space to repel the complementary dynamics contained in the interior of the state space. The conditions are formulated in terms of Lyapunov exponents and invariant probability measures and we use them to prove a robust uniform persistence result.

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Mathematics Subject Classification: Primary: 34K25; Secondary: 34K60, 92D25.

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