一类具有不同来源分布的激活-抑制剂模型的分支分析OA
Bifurcation analysis of a class of activator-inhibitor models with different source
本研究考虑了具有不同来源分布没有扩散影响下的Gierer-Meinhardt模型,当u=0,s=T=2,r=3时对应系统的分支现象.首先,分析了系统中正平衡点的个数和性质;然后,讨论了系统在正平衡点附近的分支行为,证明系统在适当参数条件下发生鞍结点分支,余维3的Bogdanov-Takens分支;并验证了系统在E01附近发生超临界Hopf分支,分支出一个稳定的极限环.
The bifurcation phenomena of the system for u=0,s=T=2,r=3 in the Gierer-Meinhardt model is considered,under the assumption of different source and without the diffusion effects.First,the number and properties of the positive equilibria in the system is analyzed.Finally,the bifurcation behavior near the positive equilibria is discussed and it demonstrates that the system undergoes saddle-node bifurcation,Bogdanov-Takens bifurcation of codimension-3 under some parameter conditions,and the system occurs a supercritical Hopf bifurcation and undergoes a stable limit cycle at E01.
贺孝英;吴奎霖
贵州大学数学与统计学院,贵州,贵阳 550025贵州大学数学与统计学院,贵州,贵阳 550025
数理科学
Gierer-Meinhardt模型鞍结点分支Hopf分支Bogdanov-Takens分支
Gierer-Meinhardt modelsaddle-node bifurcationHopf bifurcationBogdanov-Takens bifurcation
《井冈山大学学报（自然科学版）》 2026 (1)
10-22,13
国家自然科学基金项目(12361034)贵州省科技计划项目(黔科合基础-ZK[2022]一般118)
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