Hopf bifurcation of a diffusive Gause-type predator-prey model induced by time fractional-order derivatives
Hopf bifurcation of a diffusive Gause-type predator-prey model induced by time fractional-order derivatives
复制标题
时间分数阶导数引起的扩散高斯型捕食者-猎物模型的 Hopf 分岔
DOI：
10.1002/mma.5066
复制
发表时间：
2018
影响因子：
2.9
通讯作者：
Wen Xiaoqing
中科院分区：
文献类型：
--
作者：
Yin Hongwei;Wen Xiaoqing
由于种群行为具有历史记忆的特性，本文将时间分数阶导数引入扩散高斯型捕食者-猎物模型，即时间分数阶反应-扩散方程及其相应的一阶导数模型的广义形式。对于这类模型，利用演化方程理论和时间分数阶偏微分方程的比较原理，证明了其整体正解的存在唯一性。此外，我们还分别以时间分数阶普通方程和时间分数阶反应扩散方程的形式得到了Gause型捕食者-猎物模型的稳定性和Hopf分岔。结果表明，时间分数阶导数可以扩大这两个模型参数的稳定区域。通过数值模拟验证了本文的研究结果。
Since population behaviors possess the characteristic of history memory, we, in this paper, introduce time fractional‐order derivatives into a diffusive Gause‐type predator‐prey model, which is time fractional‐order reaction‐diffusion equations and a generalized form of its corresponding first‐derivative model. For this kind of model, we prove the existence and uniqueness of a global positive solution by using the theory of evolution equations and the comparison principle of time fractional‐order partial differential equations. Besides, we obtain the stability and Hopf bifurcation of the Gause‐type predator‐prey model in the forms of the time fractional‐order ordinary equations and of the time fractional‐order reaction‐diffusion equations, respectively. Our results show that the stable region of the parameters in these 2 models can be enlarged by the time fractional‐order derivatives. Some numerical simulations are made to verify our results.