一比率依赖的捕食-被捕食模型的空间斑图研究

Pattern Formation of a Ratio-dependent Predator-prey Model

研究了一带比率依赖功能性反应的捕食-被捕食模型的空间斑图.我们得到模型发生Hopf和Turing分支的临界表达式,得到发生Turing斑图发生的精确区域,并给出了数值模拟.我们的结果表明:该模型具有丰富的动力学行为,包括点状、条状以及迷宫状斑图.这些结果说明利用反应扩散方程建模是揭示空间动力学复杂性机理的一个有效工具.

We analyze the pattern formation of a ratio-dependent predator-prey system. We obtain the conditions of Hopf and Turing bifurcation in a spatial domain. In particular, exact Turing domain is. given. Also we perform a series of numerical simulations. The obtained results reveal that this system has rich dynamics, such as spotted, stripe and labyrinth pattern, which show that it is useful to use reaction-diffusion model to reveal the spatial dynamics.