  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.
