On the Sensitivity of Characteristic Roots of a Class of Parameterized Delay-Differential Neutral Systems

This paper focuses on the characterization of the asymptotic behavior of the critical characteristic roots for a class of delay-differential dynamical systems of neutral type whose coefficients smoothly depend on certain parameters. Such systems can be described by coupled delay-differential and delay-difference equations, and model time heterogeneity in propagation and transport phenomena. The asymptotic behavior of the characteristic roots is addressed by expressing the solutions as a convergent Puiseux series, which facilitates handling multiple solutions. Particular attention is paid to the way the parameters affect the stability of the delay-difference operator. Illustrative examples complete the presentation and show the effectiveness of the proposed method. © 2024 IEEE.

Asymptotic analysis; Asymptotic behaviour; Characteristic roots; Delay difference equations; Difference models; Differential dynamical systems; Differential-difference equations; Neutral systems; Neutral type; Parameterized; Transport phenomenon; Delay-sensitive applications

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