In this paper, we consider the signal-dependent diffusion and sensitivity in a chemotaxis–competition population system with two different signals in a two-dimensional bounded domain. We consider more general signal production functions and assume that the signal-dependent diffusion is a decreasing function which may be degenerate with respect to the density of the corresponding signal. We first obtain the global existence and uniform-in-time bound of classical solutions and show that the blow-up effect can be precluded for signal-dependent diffusion and sensitivity with certain properties. Then, by constructing Lyapunov functionals, we study the global attractivity of nonzero (boundary/positive) homogeneous steady states under three different strengths of competition. In particular, we obtain that the nonzero boundary constant steady states are globally asymptotically stable when they are globally attractive, which means no pattern formation occurs, while for interior constant steady state, its global attractivity can imply the global stability for some special signal production functions. Finally, numerical simulations show that for large signal sensitivity, different signal production functions can lead to various complex spatial–temporal patterns around the positive homogeneous steady state. In particular, for a given signal production mechanism, various patterns are observed for different population growth rates.

在本文中，我们考虑了在二维边界域中具有两个不同信号的趋化竞争种群系统中信号依赖的扩散和敏感性。我们考虑更一般的信号产生函数，并假设信号相关的扩散是一个递减函数，该函数可能相对于相应信号的密度而退化。我们首先获得经典解的整体存在性和时间均匀边界，并证明对于具有某些性质的信号依赖扩散和灵敏度，可以排除爆炸效应。然后，通过构造李雅普诺夫泛函，我们研究了三种不同竞争强度下非零（边界/正）齐次稳态的全局吸引性。特别是，我们得到非零边界恒定稳态当它们具有全局吸引力时是全局渐近稳定的，这意味着没有模式形成发生，而对于内部恒定稳态，其全局吸引性可以暗示某些特殊信号产生函数的全局稳定性。最后，数值模拟表明，对于较大的信号灵敏度，不同的信号产生函数可以导致正均匀稳态周围的各种复杂时空模式。特别地，对于给定的信号产生机制，对于不同的人口增长率观察到各种模式。它的全局吸引力可以暗示某些特殊信号产生功能的全局稳定性。最后，数值模拟表明，对于较大的信号灵敏度，不同的信号产生函数可以导致正均匀稳态周围的各种复杂时空模式。特别地，对于给定的信号产生机制，对于不同的人口增长率观察到各种模式。它的全局吸引力可以暗示某些特殊信号产生功能的全局稳定性。最后，数值模拟表明，对于较大的信号灵敏度，不同的信号产生函数可能导致正均匀稳态周围的各种复杂时空模式。特别地，对于给定的信号产生机制，对于不同的人口增长率观察到各种模式。