In this work, we study dynamic properties of classical solutions to a homogenous Neumann initial-boundary value problem (IBVP) for a two-species and two-stimuli chemotaxis model with/without chemical signalling loop in a 2D bounded and smooth domain. We detect the product of two species masses as a feature to determine boundedness, gradient estimate, blow-up and exponential convergence of classical solutions for the corresponding IBVP. More specifically, we first show generally a smallness on the product of both species masses, thus allowing one species mass to be suitably large, is sufficient to guarantee global boundedness, higher order gradient estimates and \(W^{j,\infty }(j\ge 1)\)-exponential convergence with rates of convergence to constant equilibria; and then, in a special case, we detect a straight line of masses on which blow-up occurs for large product of masses. Our findings provide new understandings about the underlying model, and thus, improve and extend greatly the existing knowledge relevant to this model.

在这项工作中，我们研究了具有/不具有2D有界和光滑域中的化学信号回路的两物种和两刺激趋化模型的同质Neumann初值问题（IBVP）的经典解的动力学性质。我们检测两个物种质量的乘积作为特征，以确定相应IBVP的经典解的有界性，梯度估计，爆炸和指数收敛。更具体地说，我们首先通常会显示两种物种的乘积较小，因此允许一个物种的质量适当大，足以保证全局有界性，更高阶的梯度估计和\（W ^ {j，\ infty}（ j \ ge 1）\）-指数收敛，收敛速度为恒定均衡；然后，在特殊情况下，我们检测到一条直线，该直线在大块质量的产品上会发生爆炸。我们的发现为基础模型提供了新的理解，从而大大改善和扩展了与该模型相关的现有知识。