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具有Crowley-Martin功能性反应的偏害系统的稳定性和分支分析
魏臻, 甘胜进
福建师范大学福清分校 电子与信息工程学院, 福建 福清 350300
摘要:
针对一类具有Crowlay-Martin功能性反应的偏害系统的动力学行为,研究其系统平衡点的局部稳定性。利用Sotomayor定理,证明了在适当的条件下存在鞍结分支和跨临界分支,并通过数值模拟验证了主要结论。
关键词:  鞍结分支  跨临界分支  偏害模型  Crowley-Martin功能性反应
DOI:10.3969/J.ISSN.1000-5137.2020.05.003
分类号:O19
基金项目:The Natural Science Foundation of Fujian Province (2018J01662)
Stability and bifurcation analysis of an amensalism model with Crowley-Martin type functional response
WEI Zhen, GAN Shengjin
School of Electronic and Information Engineering, Fuqing Branch of Fujian Normal University, Fuqing 350300, Fujian, China
Abstract:
In this paper, an amensalism model with Crowley-Martin type functional response is proposed. The existence and stability of all possible equilibria of the system are investigated. We also prove that there are saddle-node bifurcation and transcritical bifurcation under suitable conditions by Sotomayor's theorem. An example with its numeric simulations is given to verify our main results.
Key words:  saddle-node bifurcation  transcritical bifurcation  amensalism model  Crowley-Martin type functional response