This paper is concerned with the existence and stability of steady state solutions for the SKT biological competition model with cross-diffusion. By applying the detailed spectral analysis and in virtue of the bifurcating direction to the limiting system as the cross diffusion rate tends to infinity, it is proved the stability/instability of the nontrivial positive steady states with some special bifurcating structure. Further, the existence and stability/instability of the corresponding nontrivial positive steady states for the original cross-diffusion system are proved by applying perturbation argument.

中文翻译：

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具有大交叉扩散的 SKT 模型非平凡正稳态的稳定性

本文关注的是具有交叉扩散的SKT生物竞争模型稳态解的存在性和稳定性。通过应用详细的谱分析，并根据交叉扩散速率趋于无穷大的极限系统的分岔方向，证明了具有一些特殊分岔结构的非平凡正稳态的稳定性/不稳定性。此外，通过应用微扰论证证明了原始交叉扩散系统对应的非平凡正稳态的存在性和稳定性/不稳定性。