This paper deals with the global stability of the following density-suppressed motility system

in a bounded domain \(\Omega \subset \mathbb {R}^{2}\) with smooth boundary, where the motility function \(\varphi (v)\) is positive. If \(\varphi (v)\) has the lower-upper bound, we can obtain that this system possesses a unique bounded classical solution. Moreover, we can obtain that the global solution (u, v, w, z) will exponentially converge to the equilibrium \((\overline{u}_{0},\overline{v}_{0}+\overline{w}_{0},0,\overline{u}_{0})\) as \(t\rightarrow +\infty \), where \(\overline{f}_{0}=\frac{1}{|\Omega |}\int _{\Omega }f_{0}(x)\mathrm{d}x\).

本文研究了以下密度抑制运动系统的全局稳定性

在具有平滑边界的有界域\（\ Omega \ subset \ mathbb {R} ^ {2} \）中，其中运动函数\（\ varphi（v）\）为正。如果\（\ varphi（v）\）具有下界，我们可以得到该系统具有唯一有界经典解。此外，我们可以获得全局解（u，  v，  w，  z）将指数收敛于平衡\（（\ overline {u} _ {0}，\ overline {v} _ {0} + \ overline { w} _ {0}，0，\ overline {u} _ {0}）\）如\（t \ rightarrow + \ infty \），其中\（\ overline {f} _ {0} = \ frac {1 } {| \ Omega |} \ int _ {\ Omega} f_ {0}（x）\ mathrm {d} x \）。