一类具有时滞且带有捕食者相互残杀项的捕食模型的时空斑图

Pattern Formation Induced by Time Delay in a Predator-Prey Model with Predator Cannibalism

研究了一类具有时滞且带有捕食者相互残杀项的食饵-捕食者模型的动力学行为.通过数学分析,发现了不同类型的不稳定性,并且详细的给出了图灵不稳定的条件.通过一系列的数值模拟,得到了参数空间中丰富的图灵结构,分别有点状斑图、条状斑图以及点状和条状共存的斑图结构.这些结果表明,受时滞影响的带有捕食相互残杀项的捕食模型具有丰富的动力学,揭示了模型在实际生活中是非常有用的.

A predator-prey model with predator cannibalism and time delay was considered. By mathematical analysis, different types of instability are found and the conditions for emerg- ing Turing instability are given in detail. The spatial patterns via numerical simulations are illustrated, which show that the model dynamics exhibits rich parameter space Turing struc- tures, respectively, spots, stripe-like patterns, and coexistence of both. The obtain results show that this system has rich dynamics, these patterns shows that it is useful for predation model both with predator cannibalism and a delay effect to reveal the spatial dynamics in the real model.