College of Science, University of Shanghai for Science and Technology, Shanghai 200093, People's Republic China.
Chaos. 2013 Sep;23(3):033102. doi: 10.1063/1.4812724.
In this paper, a spatial predator-prey model with herd behavior in prey population and quadratic mortality in predator population is investigated. By the linear stability analysis, we obtain the condition for stationary pattern. Moreover, using standard multiple-scale analysis, we establish the amplitude equations for the excited modes, which determine the stability of amplitudes towards uniform and inhomogeneous perturbations. By numerical simulations, we find that the model exhibits complex pattern replication: spotted pattern, stripe pattern, and coexistence of the two. The results may enrich the pattern dynamics in predator-prey models and help us to better understand the dynamics of predator-prey interactions in a real environment.
本文研究了具有群体行为的食饵种群和二次死亡率的捕食者种群的空间捕食者-食饵模型。通过线性稳定性分析，我们得到了稳定模式的条件。此外，通过标准的多尺度分析，我们建立了激发模式的幅度方程，这些方程确定了幅度对均匀和非均匀微扰的稳定性。通过数值模拟，我们发现模型表现出复杂的模式复制：斑点模式、条纹模式和两者共存。这些结果可能丰富捕食者-食饵模型中的模式动力学，并帮助我们更好地理解真实环境中捕食者-食饵相互作用的动力学。
