一类捕食食饵系统中交叉扩散诱导的图灵不稳和斑图

摘要

The phenomenon of pattern formation for predator-prey model with cross-diffusion is considered.We prove that cross-diffusion can destabilize the positive equilibrium which is stable for the self-diffusion reaction system.We also derive cross-diffusion-driven instability conditions.Moreover,our numerical simulations support our theoretical findings and exhibit that the model has complex spatial patterns:stripe pattern,spotted pattern and their coexistence.These results show that the cross-diffusion plays an important role in the pattern formation.%研究了一类具有交叉扩散的捕食食饵模型的斑图形成.证明了交叉扩散破坏了正平衡点的稳定性,得到了交叉扩散导致不稳的条件.另外,数值模拟结果不仅支持了该理论,还显示模型具有复杂的空间斑图:条状斑图、点状斑图以及点条混合斑图.研究结果表明交叉扩散在斑图的形成中起着重要的作用.