Dissipativity Analysis of General Linear Methods for Coupled Systems of Nonlinear Functional Differential and Functional Equations
DOI: https://doi.org/10.62517/jnse.202517508
Author(s)
Zhang Peng
Affiliation(s)
School of Mathematics, Qilu Normal University, Jinan, Shandong, China
Abstract
The analysis of long-term behavior in nonlinear systems is one of the core contents in modern applied mathematics. Its key characteristic is dissipativity, which implies that the system exhibits a certain form of global boundedness or the ultimate decay of energy, ensuring that the system will eventually enter a globally attracting set. Studying dissipativity is of great significance for analyzing the stability and controllability of nonlinear functional systems. Currently, functional differential equations depend not only on the current state but also on past states. When coupled with other types of equations, dissipativity analysis becomes relatively difficult and extremely complex. For such coupled systems, it is necessary to analyze their numerical methods and identify appropriate research tools.
Keywords
Nonlinear Functional Differential and Functional Equations; Coupled Systems; General Linear Methods; Dissipativity
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