FitzHugh-Nagumo方程的分歧  

On the bifurcation of the FitzHugh-Nagumo equation

作　　者：闫东明 YAN Dong-ming(School of Data Sciences,Zhejiang University of Finance and Economics,Hangzhou 310018,China)

机构地区：[1]浙江财经大学数据科学学院,浙江杭州310018

出　　处：《高校应用数学学报（A辑）》2020年第3期265-274,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：浙江省一流学科A类(浙江财经大学统计学)资助。

摘　　要：运用非线性分歧理论,研究FitzHugh-Nagumo方程的定态分歧和Hopf分歧.证明了FitzHugh-Nagumo方程在适当条件下有定态分歧发生,此时FitzHugh-Nagumo方程的定态方程有非平凡解存在.另外还证明了FitzHugh-Nagumo方程在适当的条件下有Hopf分歧发生,此时该方程从平凡解分歧出非平凡的周期解.最后分析得出影响FitzHugh-Nagumo方程分歧发生的主要因素是离子电压门控通道打开与关闭的延迟反应的快慢.理论分析所得结果与实验现象是相一致的.In this paper, the steady state bifurcation and Hopf bifurcation of the FitzHughNagumo equation are investigated. By using the nonlinear bifurcation theory, steady state bifurcation occurs under proper conditions have been proved, which means that this system bifurcates from the trivial solution to the nontrivial solution. Furthermore, Hopf bifurcation occurs under proper conditions have been proved, which means that this system bifurcates from the trivial solution to the nontrivial periodic solution. Finally, delayed response of the channels is the key factor that affects the bifurcation of FitzHugh-Nagumo equation are obtained. The calculated results are consistent with the experimental results.

关 键 词：FITZHUGH-NAGUMO方程 分歧理论 定态分歧 HOPF分歧 周期解 

分 类 号：O175.29[理学—数学]