基于快慢系统的生态传染病模型的分析

冯永清; 靳祯

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基于快慢系统的生态传染病模型的分析

更新时间：2026-09-14

- 基于快慢系统的生态传染病模型的分析
- 基于快慢系统的生态传染病模型的分析
- Issue 1, (2011)
- 作者机构：
  
  中北大学理学院
- 作者简介：
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- Published：2011
- 稿件说明：
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冯永清, 靳祯. 基于快慢系统的生态传染病模型的分析[J]. 2011, (1).
DOI：

冯永清, 靳祯. 基于快慢系统的生态传染病模型的分析[J]. 2011, (1). DOI：

摘要

建立了食饵迁移捕食者染病的生态传染病模型.考虑了两个时间尺度

建立了食饵迁移捕食者染病的快系统和种群间相互作用的慢系统

并利用快系统的平衡降低了模型的维数.通过分析Jacobian矩阵

得出了系统正平衡点的局部渐近稳定性;并通过排除周期轨的存在

进一步得出了正平衡点的全局渐近稳定性.

Abstract

The eco-epidemiological model with the disease in the predators and the migration of prey was formulated.By considering two time scales

two systems were established

one is of fast time scale considering prey migration and infected predators;the other is of slow one considering the interactions between populations.The system dimension was reduced with the fast time scale.By analyzing the Jacobian matrix

the positive equilibrias' local asymptotical stability was obtained.Furthermore

the global asymptotical stability was obtained by excluding the existence of periodic orbit.

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