带Lotka-Volterra互惠源的多种群趋化模型的稳定性

胡晓丽,伏升茂

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (6) : 1541-1554.

PDF(366 KB)
PDF(366 KB)
系统科学与数学 ›› 2017, Vol. 37 ›› Issue (6) : 1541-1554. DOI: 10.12341/jssms13208
论文

带Lotka-Volterra互惠源的多种群趋化模型的稳定性

    胡晓丽 ,伏升茂
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Stability in a Multi-Species Chemotaxis Model with  Lotka-Volterra Cooperative Source

    HU Xiaoli ,FU Shengmao
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摘要

主要研究带 Lotka-Volterra 互惠源项的多种群趋化模型的唯一正平衡点的稳定性. 首先应用非奇M-矩阵理论给出该模型存在唯一正平衡点的充分条件; 然后用线性化方法分析正平衡点的局部稳定性; 最后结合该模型与一个相应的常微分方程组之间的关系讨论正平衡点的全局渐近稳定性.

Abstract

In this paper, we mainly study the stability of a unique positive equilibrium point for a multi-species chemotaxis model with Lotka-Volterra cooperative source. Firstly, we give a sufficient condition to guarantee the existence and uniqueness of positive equilibrium point in the model by applying the nonsingular M-matrix theory. Then, by using the linearization, the local stability of the unique positive equilibrium point is proved. Finally, we discuss the global asymptotical stability of the positive equilibrium point by the relationship between this model and a corresponding system of ordinary differential equations.

关键词

多种群趋化模型 / 互惠 / 正平衡点 / 稳定性.

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胡晓丽 , 伏升茂. 带Lotka-Volterra互惠源的多种群趋化模型的稳定性. 系统科学与数学, 2017, 37(6): 1541-1554. https://doi.org/10.12341/jssms13208
HU Xiaoli , FU Shengmao. Stability in a Multi-Species Chemotaxis Model with  Lotka-Volterra Cooperative Source. Journal of Systems Science and Mathematical Sciences, 2017, 37(6): 1541-1554 https://doi.org/10.12341/jssms13208
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