Turing instability and pattern induced by cross-diffusion in a predator-prey system

Journal of Shanghai Normal University (Natural Sciences)

Peng Yahong¹  Wang Qiufang¹ 

[1] College of Science, Donghua University, Shanghai 201620, China;

关键词: predator-prey system;    cross-diffusion;    Turing instability;    pattern formation;   

DOI  :  10.3969/J.ISSN.100-5137.2018.03.008

来源: DOAJ

【 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.

【 授权许可】

Unknown