Delayed feedback induced complex dynamics in an Escherichia coli and Tetrahymena system
Delayed feedback induced complex dynamics in an Escherichia coli and Tetrahymena system
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DOI：
10.1007/s11071-018-4434-4
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发表时间：
2018-06
影响因子：
5.6
通讯作者：
Yueping Dong;Moitri Sen;M. Banerjee;Y. Takeuchi;S. Nakaoka
中科院分区：
文献类型：
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作者：
Yueping Dong;Moitri Sen;M. Banerjee;Y. Takeuchi;S. Nakaoka
在特定的环境中，细菌物种的数量，如大肠杆菌，部分受原生动物物种捕食的调节。捕食者和被捕食者之间的相互作用并不简单，因为被捕食者已经获得了抵抗捕食的防御机制。已知有多种防御机制，例如，产生毒素作为负反馈效应来抑制捕食者物种。另一方面，捕食者物种对被捕食者物种也会产生负反馈效应。在负反馈效应存在的情况下产生的种群动态会受到反馈控制的强度和时间延迟的显着影响，这自然地会发生，直到负反馈效应生效。在本文中，我们建立了一个数学模型来研究志贺毒素产生和中性粒细胞募集的延迟反馈控制的大肠杆菌和四膜虫之间的相互作用。通过应用准稳态近似，将所提出的模型归结为具有两个离散时滞的Lotka-Volterra型捕食-食饵系统。通过研究特征方程的根的分布，研究了特征方程的局部稳定性和Hopf分支。我们提供了一个清晰的分类框架来检测当存在两个时滞时发生Hopf分支的可能性。通过数值模拟对分析结果进行了验证。结果表明，随着负反馈控制系数的增加，两时滞参数平面内共存平衡的不稳定区域总是扩大，特别是四膜种群的反馈控制对共存平衡的不稳定起主导作用。此外，我们还观察到了一些有趣的现象，如增峰分叉、准周期振荡和混沌。
Abundances of bacterial species such asEscherichia coliin a given environment are partly regulated by predation by protozoa species. Interactions among prey and predator species are not simple since a prey species has acquired defense mechanism against predation. A variety of defense mechanisms are known, for instance, production of toxin as a negative feedback effect to suppress predator species. On the other hand, negative feedback effects can be generated by a predator species to the prey species. The resulting population dynamics under the presence of negative feedback effects would be significantly affected by the strength of feedback control and time delay which naturally occurs until negative feedback effects become effective. In this paper, we develop a mathematical model to investigate the interaction between Shiga-toxin producingEscherichia coliandTetrahymenawith delayed feedback controls by production of Shiga-toxin and recruitment of neutrophils. By applying the quasi-steady-state approximation, the proposed model is reduced to a Lotka–Volterra type predator–prey system with two discrete delays. By investigating the distribution of the roots of the characteristic equation, the local stability as well as Hopf-bifurcation are studied. We provide a clear classification framework to detect the possibility of Hopf-bifurcation when two delays are present. Numerical simulations are carried out to verify the analytical results. Our findings reveal that the instability regions of coexistence equilibrium in two delay parameters plane always enlarge with the increase in negative feedback control coefficients, and especially the feedback controls onTetrahymenapopulation play a dominant role in the destabilization of coexistence equilibrium. Besides, we observe some interesting phenomena such as peak-adding bifurcation, quasi-periodic oscillation and chaos.