Abstract
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for delay-independent stability of these equations, called intrinsic stability, showing global exponential stability for a large class of nonautonomous nonlinear systems. Our approach is able to incorporate bounded time-varying delays, including those with certain types of discontinuities. The approach we take to prove this result is novel, associating the delay differential equation with a sequence of finite-dimensional matrices of increasing size and using the graph-theoretic technique of isospectral reduction to analyze this sequence. We give an application of these results to the problem of determining consistency for delayed reservoir computers.
Degree
MS
College and Department
Computational, Mathematical, and Physical Sciences; Mathematics
Rights
https://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Leishman, Quinlan, "A New Approach to Stability of Delay Differential Equations with Time-Varying Delays via Isospectral Reduction" (2025). Theses and Dissertations. 10923.
https://scholarsarchive.byu.edu/etd/10923
Date Submitted
2025-07-14
Document Type
Thesis
Permanent Link
https://apps.lib.byu.edu/arks/ark:/34234/q2c6ebb518
Keywords
delay differential equations, time delays, stability, isospectral reduction, reservoir computing
Language
english