With successive coupling of two taxis mechanisms and with density-dependent taxis sensitivities, the producer–scrounger system $\left\{\begin{array}{ccc}{u}_t\hfill & \hfill =\hfill & \Delta u-\nabla \cdot (u{(u+1)}^{\beta -1}\nabla w),\hfill \\ v_t\hfill & \hfill =\hfill & \Delta v-\nabla \cdot (v{(v+1)}^{\alpha -1}\nabla u),\hfill \\ w_t\hfill & \hfill =\hfill & \Delta w-(u+v)w-\lambda w+g(x,t),\hfill \end{array}\right.$is considered in a bounded smooth domain $\Omega \subset {\mathbb{R}}^n$ ( $n\ge 2$), where $\alpha \le 1$, $\beta \le 1$ and $\lambda >0$ are prescribed parameters, and $g$ is a given $C^1$-smooth function. It is shown that whenever $\beta <1\text{and}\alpha <\frac{n+2}{2n}$and $g$ satisfies ${\int }_t^{t+1}{\int }_{\Omega }{g}^2\to 0$ as $t\to \infty$, for all suitably regular initial data $(u_0,v_0,w_0)$ the corresponding homogeneous Neumann initial–boundary problem admits a global classical solution $(u,v,w)$ that converges to $(\frac{1}{\left|\Omega \right|}{\int }_{\Omega }{u}_0,\frac{1}{\left|\Omega \right|}{\int }_{\Omega }{v}_0,0)$ in the large time limit.

通过两个滑行机制的连续耦合以及与密度相关的滑行灵敏度，生产者-辅助系统 $\left\{\begin{array}{ccc}{ü}_{Ť}\hfill & \hfill =\hfill & \Delta ü-\nabla \cdot （ü{（ü+\mathrm{1个}）}^{\beta -\mathrm{1个}}\nabla w），\hfill \\ v_{Ť}\hfill & \hfill =\hfill & \Delta v-\nabla \cdot （v{（v+\mathrm{1个}）}^{\alpha -\mathrm{1个}}\nabla ü），\hfill \\ w_{Ť}\hfill & \hfill =\hfill & \Delta w-（ü+v）w-\lambda w+G（X，Ť），\hfill \end{array}\right.$被认为是有界光滑域 $\Omega \subset {\mathbb{[R}}^{ñ}$ （ $ñ\ge 2$），在哪里 $\alpha \le \mathrm{1个}$， $\beta \le \mathrm{1个}$ 和 $\lambda >0$ 是规定的参数，并且 $G$ 是给定的 $C^{\mathrm{1个}}$-平滑功能。结果表明，每当$\beta <\mathrm{1个}\text{和}\alpha <\frac{ñ+2}{2ñ}$和 $G$ 满足 ${\int }_{Ť}^{Ť+\mathrm{1个}}{\int }_{\Omega }{G}^2\to 0$ 如 $Ť\to \infty$，用于所有适当的常规初始数据 $（{ü}_0，v_0，w_0）$ 相应的齐次Neumann初-边界问题承认了全局经典解 $（ü，v，w）$ 收敛到 $（\frac{\mathrm{1个}}{\left|\Omega \right|}{\int }_{\Omega }{ü}_0，\frac{\mathrm{1个}}{\left|\Omega \right|}{\int }_{\Omega }{v}_0，0）$ 在很大的时间限制内。