Identifiability and Global Stability Analysis on Some Partial Differential Algebraic System

TL;DR

This paper investigates the identifiability and global stability of certain high-dimensional singular partial differential algebraic systems, providing theoretical analysis and numerical validation in ecological applications.

Contribution

It introduces a novel approach combining eigenvalue theory and spectrum analysis for stability assessment of PDAEs with boundary conditions.

Findings

Global stability results established for the studied PDAEs.

Numerical simulations demonstrate applicability to ecological systems.

Spectrum-based state space description enhances understanding of system behavior.

Abstract

We analysis some singular partial differential equations systems(PDAEs) with boundary conditions in high dimension bounded domain with sufficiently smooth boundary. With the eigenvalue theory of PDE the systems initially is formulated as an infinite-dimensional singular systems. The state space description of the system is built according to the spectrum structure and convergence analysis of the PDAEs. Some global stability results are provided. The applicability of the proposed approach is evaluated in numerical simulations on some wetland conservation system with social behaviour.