Modeling Boyciana-fish-human Interaction with Partial Differential Algebraic Equations

TL;DR

This paper develops a PDE-DAE model to analyze boyciana-fish-human interactions, examining stability, persistence, and human interference effects, validated with real data and numerical simulations.

Contribution

It introduces a novel PDAEs framework for modeling complex ecological interactions involving human activity, with analytical and numerical validation using real-world data.

Findings

Identified three human interference conditions affecting the system.

Analyzed stability and persistence properties of the model.

Predicted wetland boyciana population dynamics with real data.

Abstract

With human social behaviors influence, some boyciana-fish reaction-diffusion system coupled with elliptic human distribution equation is considered. Firstly, under homogeneous Neumann boundary conditions and ratio-dependent functional response the system can be described as a nonlinear partial differential algebraic equations (PDAEs) and the corresponding linearized system is discussed with singular system theorem. In what follows we discuss the elliptic subsystem and show that the three kinds of nonnegative are corresponded to three different human interference conditions: human free, overdevelopment and regular human activity. Next we examine the system persistence properties: absorbtion region and the stability of positive steady states of three systems. And the diffusion-driven unstable property is also discussed. Moreover, we propose some energy estimation discussion to reveal the dynamic property among the boyciana-fish-human interaction systems.Finally, using the realistic data collected in the past fourteen years, by PDAEs model parameter optimization, we carry out some predicted results about wetland boyciana population. The applicability of the proposed approaches are confirmed analytically and are evaluated in numerical simulations.