Existence of spatial patterns in a predator-prey model with self- and cross-diffusion
Existence of spatial patterns in a predator-prey model with self- and cross-diffusion
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DOI：
10.1016/j.amc.2013.10.005
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Lakshmi Narayan Guin
中科院分区：
文献类型：
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作者：
Lakshmi Narayan Guin
本文在二维比率依赖的捕食者-食饵模型的框架下，研究了具有交叉扩散的反应扩散方程的时空动力学。得到了扩散驱动不稳定性的条件，并得到了参数空间中的图灵空间。此外，还讨论了唯一正齐次无扩散平衡态的局部和全局渐近稳定性的判据。数值模拟进行，以验证所获得的分析结果的可行性。不同类型的空间模式，通过扩散驱动的不稳定性的建议模型进行了描绘和分析。最后，本文结束了关于交叉扩散和模式问题的分析的生物相关性的外部讨论。
In this work, we investigate the spatiotemporal dynamics of reaction–diffusion equations subject to cross-diffusion in the frame of a two-dimensional ratio-dependent predator–prey model. The conditions for diffusion-driven instability are obtained and the Turing space in the parameters space is achieved. Moreover, the criteria for local and global asymptotic stability of the unique positive homogeneous steady state without diffusion are discussed. Numerical simulations are carried out in order to validate the feasibility of the obtained analytical findings. Different types of spatial patterns through diffusion-driven instability of the proposed model are portrayed and analysed. Lastly, the paper finishes with an external discussion of biological relevance of the analysis regarding cross-diffusion and pattern issues.