Wang Caiyun, Chang Lili, Liu Huifeng
Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, Shan'xi, China.
Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, China.
PLoS One. 2016 Mar 1;11(3):e0150503. doi: 10.1371/journal.pone.0150503. eCollection 2016.
Time delay due to maturation time, capturing time or other reasons widely exists in biological systems. In this paper, a predator-prey system of Leslie type with diffusion and time delay is studied based on mathematical analysis and numerical simulations. Conditions for both delay induced and diffusion induced Turing instability are obtained by using bifurcation theory. Furthermore, a series of numerical simulations are performed to illustrate the spatial patterns, which reveal the information of density changes of both prey and predator populations. The obtained results show that the interaction between diffusion and time delay may give rise to rich dynamics in ecosystems.
由于成熟时间、捕获时间或其他原因导致的时间延迟在生物系统中广泛存在。本文基于数学分析和数值模拟，研究了一个具有扩散和时间延迟的莱斯利型捕食者 - 猎物系统。利用分岔理论得到了延迟诱导和扩散诱导的图灵不稳定性条件。此外，进行了一系列数值模拟以说明空间模式，这些模式揭示了猎物和捕食者种群密度变化的信息。所得结果表明，扩散和时间延迟之间的相互作用可能在生态系统中产生丰富的动力学行为。
