When the asymptotic spreading for classical monostable Lotka-Volterra competition diffusion systems is concerned, extinction or persistence of the two competitive species is completely determined by the dynamics of the corresponding kinetic systems, while the size of initial values does not affect the final states. The purpose of this paper is to demonstrate the rich dynamics induced by the initial values in a class of degenerate competition diffusion systems with weak Allee effect. We present various extinction or persistence results by selecting different initial values although the corresponding kinetic system is fixed, which also implies the existence of balance between degenerate nonlinear reaction and diffusion. For example, even if the positive steady state of the corresponding kinetic system is globally asymptotically stable, we observe four different spreading-vanishing phenomena by selecting different initial values. In addition, the interspecific competition of one species may be harmful to the persistence of the other species by taking proper initial values. Our results show that the superior competitor in the sense of the corresponding kinetic system is not always unbeatable, it can be wiped out by the inferior competitor in the sense of the corresponding kinetic system depending on the size of initial habitats as well as the intensity of Allee effect.

中文翻译：

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初始值对退化扩散竞争系统中的灭绝或持久性的影响。

当考虑经典单稳态Lotka-Volterra竞争扩散系统的渐近扩散时，两个竞争物种的灭绝或持续性完全由相应动力学系统的动力学决定，而初始值的大小并不影响最终状态。本文的目的是证明一类具有弱Allee效应的退化竞争扩散系统的初始值引起的丰富动力学。尽管固定了相应的动力学系统，但通过选择不同的初始值，我们提出了各种消光或持久性结果，这也意味着退化的非线性反应与扩散之间存在平衡。例如，即使相应动力学系统的正稳态是全局渐近稳定的，通过选择不同的初始值，我们观察到四种不同的消失消失现象。另外，通过采用适当的初始值，一个物种的种间竞争可能对另一物种的持久性有害。我们的结果表明，在相应动力学系统意义上的优胜者并不总是无与伦比的，它可以在相应动力学系统意义上被劣等竞争对手淘汰，具体取决于初始栖息地的大小以及阿利效应。