This paper deals with the following competitive two-species chemotaxis system with two chemicals

$ \left\{ {\begin{array}{*{20}{l}}{{u_t} = \Delta u - {\chi _1}\nabla \cdot (u\nabla v) + {\mu _1}u\left( {1 - u - {a_1}w} \right),}&{x \in \Omega ,t > 0,}\\{0 = \Delta v - v + w,}&{x \in \Omega ,t > 0,}\\{{w_t} = \Delta w - {\chi _2}\nabla \cdot (w\nabla z) + {\mu _2}w\left( {1 - w - {a_2}u} \right),}&{x \in \Omega ,t > 0,}\\{0 = \Delta z - z + u,}&{x \in \Omega ,t > 0}\end{array}} \right. $

中文翻译：

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具有两种化学物质的两种物种趋化系统的有界性和稳定性的新结果

本文涉及以下具有两种化学物质的竞争性两种物质趋化系统

$ \ left \ {{\ begin {array} {* {20} {l}} {{u_t} = \ Delta u-{\ chi _1} \ nabla \ cdot（u \ nabla v）+ {\ mu _1} u \ left（{1-u-{a_1} w} \ right），}＆{x \ in \ Omega，t> 0，} \\ {0 = \ Delta v-v + w，}＆{x \在\ Omega中，t> 0，} \\ {{w_t} = \ Delta w-{\ chi _2} \ nabla \ cdot（w \ nabla z）+ {\ mu _2} w \ left（{1- w- {a_2} u} \ right），}＆{x \ in \ Omega，t> 0，} \\ {0 = \ Delta z-z + u，}＆{x \ in \ Omega，t> 0} \ end {array}} \ right。$