Pattern formation in a ratio-dependent predator-prey model with cross-diffusion

作者：

Highlights：

• Investigate the effect of the cross-diffusion on the patterns of a ratio-dependent predator-prey model.

• Find that the cross-diffusion has the important influence on the pattern formation.

• Theoretically study the stability of patterns driven by cross-diffusion using the weakly nonlinear analysis method.

• Numerically investigate the spot, stripe and mixed spot-stripe patterns induced by the cross-diffusion.

摘要

•Investigate the effect of the cross-diffusion on the patterns of a ratio-dependent predator-prey model.•Find that the cross-diffusion has the important influence on the pattern formation.•Theoretically study the stability of patterns driven by cross-diffusion using the weakly nonlinear analysis method.•Numerically investigate the spot, stripe and mixed spot-stripe patterns induced by the cross-diffusion.

论文关键词：Predator-prey model,Cross-diffusion,Turing instability,Amplitude equations,Pattern formation

论文评审过程：Received 8 December 2017, Revised 26 February 2018, Accepted 5 March 2018, Available online 27 March 2018, Version of Record 27 March 2018.

论文官网地址：https://doi.org/10.1016/j.amc.2018.03.033