Spatially inhomogeneous periodic patterns induced by distributed memory in the memory-based single population model
Spatially inhomogeneous periodic patterns induced by distributed memory in the memory-based single population model
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DOI：
10.1016/j.aml.2022.108490
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发表时间：
2022-11
期刊：
影响因子：
--
通讯作者：
Jiong Lin;Yongli Song
中科院分区：
文献类型：
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作者：
Jiong Lin;Yongli Song
本文研究了基于记忆的扩散单种群模型中分布时滞对稳定性和时空动力学的影响。在相应常微分方程的正平衡点局部渐近稳定的假设下，证明了弱核不影响该正常定态的稳定性，但对于强核，记忆扩散的扩散速率和分布时滞的综合作用会影响其稳定性并导致丰富的动力学.对于强核，给出了系统稳定、Hopf分支和双Hopf分支的理论条件。
In this paper, we investigate the influence of the distributed delay on the stability and spatiotemporal dynamics in the memory-based diffusion single population model. Under the assumption that the positive equilibrium of the corresponding ordinary differential equation is locally asymptotically stable, it has been shown that the weak kernel does not affect the stability of this positive constant steady state, but for the strong kernel, the combined effect of the diffusion rate of the memory diffusion and the distributed delay can affect the stability and lead to the rich dynamics. For the strong kernel, the theoretical conditions for the stability, Hopf bifurcation and double Hopf bifurcation are explicitly determined.