A kind of bifurcation of limit cycle from nilpotent critical point

2016/01/12 by Yirong Liu, Feng Li, Liu, Yirong +1
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1601.02826

openalex publication_date 2016/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, an interesting and new bifurcation phenomenon that limit cycles could be bifurcated from nilpotent node (focus) by changing its stability was investigated. It is different from lowing its multiplicity in order to get limit cycles. We prove that n²+n-1 limit cycles could be bifurcated by this way for 2n+1 degree system. Moreover, this upper bound could be reached. At last, we give two examples to show that N(3)=1 and N(5)=5.

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