一类广义Fisher方程的稳定性和动态分歧

Stability and dynamical bifurcation of a generalized Fisher equation

作者：张强(中国民用航空飞行学院计算机学院)；曾艳(中国民用航空飞行学院计算机学院)；周艳红(中国民用航空飞行学院计算机学院)

Author：Zhang Qiang(College of Computer Science, Civil Aviation Flight University of China)；Zeng Yan(College of Computer Science, Civil Aviation Flight University of China)；Zhou Yan-Hong(College of Computer Science, Civil Aviation Flight University of China)

收稿日期：2018-06-06 年卷（期）页码：2019,56(2):222-226

期刊名称：四川大学学报: 自然科学版

Journal Name：Journal of Sichuan University (Natural Science Edition)

关键字：Fisher方程；动态分歧；中心流形约化；吸引子分歧

Key words：Fisher equation; Dynamical bifurcation; Center manifold reduction; Attractor bifurcation

基金项目：国家自然科学基金(31300853); 中国民用航空飞行学院青年基金(Q2014-54)

中文摘要

本文研究了一类广义Fisher方程的动态分歧和解的稳定性. 利用中心流形约化方法和吸引子分歧理论,本文得到了动态分歧的完整判据、类型以及性质，并给出了吸引域的某些刻画, 补充和完善了已有文献的结果.数值模拟验证了理论分析的正确性.

英文摘要

This research studies the dynamic bifurcation and stability of solutions for a generalized Fisher equation. The complete criterion, types and properties of dynamical bifurcation are obtained by center manifold reduction method and attractor bifurcation theory. Some characterizations of basins of attractors are given. These results improve the known results.Numerical simulations are provided to verify the theoretical analysis.

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论文摘要

一类广义Fisher方程的稳定性和动态分歧

Stability and dynamical bifurcation of a generalized Fisher equation