A practical approach to computing Lyapunov exponents of renewal and delay equations

Dimitri Breda; Davide Liessi; Dimitri Breda; Davide Liessi

doi:10.3934/mbe.2024053

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 1249-1269. doi: 10.3934/mbe.2024053

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A practical approach to computing Lyapunov exponents of renewal and delay equations

Dimitri Breda ,
Davide Liessi ^,

CDLab – Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze 206, 33100 Udine, Italy

Received: 13 October 2023 Revised: 01 December 2023 Accepted: 06 December 2023 Published: 26 December 2023

We propose a method for computing the Lyapunov exponents of renewal equations (delay equations of Volterra type) and of coupled systems of renewal and delay differential equations. The method consists of the reformulation of the delay equation as an abstract differential equation, the reduction of the latter to a system of ordinary differential equations via pseudospectral collocation and the application of the standard discrete QR method. The effectiveness of the method is shown experimentally and a MATLAB implementation is provided.
- Lyapunov exponents,
- delay equations,
- renewal equations,
- pseudospectral collocation,
- discrete QR method,
- abstract differential equation
Citation: Dimitri Breda, Davide Liessi. A practical approach to computing Lyapunov exponents of renewal and delay equations[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 1249-1269. doi: 10.3934/mbe.2024053

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Abstract

We propose a method for computing the Lyapunov exponents of renewal equations (delay equations of Volterra type) and of coupled systems of renewal and delay differential equations. The method consists of the reformulation of the delay equation as an abstract differential equation, the reduction of the latter to a system of ordinary differential equations via pseudospectral collocation and the application of the standard discrete QR method. The effectiveness of the method is shown experimentally and a MATLAB implementation is provided.

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