The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or unbounded boundary. Such a model with a free boundary describes the spreading of a new or invasive species subject to the influence of some chemical substances in an environment with a free boundary representing the spreading front. In this first of the series, we investigated the dynamical behaviors of logistic type chemotaxis models on the half line $\mathbb{R}^+$, which are formally corresponding limit systems of the free boundary problems. In the second of the series, we establish the spreading-vanishing dichotomy in chemoattraction-repulsion systems with a free boundary as well as with double free boundaries.

中文翻译：

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具有自由边界或无边界的物流型吸引-排斥趋化系统。二、具有自由边界的域中的传播-消失二分法

目前的系列研究论文是在具有自由边界或无界边界的一个空间维度上研究逻辑型趋化模型中的渐近动力学。这种具有自由边界的模型描述了受某些化学物质影响的新物种或入侵物种在环境中的传播，自由边界代表传播前沿。在本系列的第一篇中，我们研究了逻辑型趋化模型在半线 $\mathbb{R}^+$ 上的动力学行为，它们是自由边界问题的形式上对应的极限系统。在该系列的第二部分，我们在具有自由边界和双自由边界的化学吸引-排斥系统中建立了扩散-消失二分法。