Analytical approximation of cuspidal loops using a nonlinear time transformation method
作者：
Highlights：
• We consider cuspidal loops, i.e., homoclinic orbits to cuspidal singular points.
• A very efficient iterative method with the nonlinear time transformation method is developed.
• A perturbation solution up to any desired order for this codimension-3 bifurcation is attained.
• Precise approximations in the phase space for this connecting orbit are also obtained.
• This higher-order approximation is acquired for the first time in the literature.
摘要
•We consider cuspidal loops, i.e., homoclinic orbits to cuspidal singular points.•A very efficient iterative method with the nonlinear time transformation method is developed.•A perturbation solution up to any desired order for this codimension-3 bifurcation is attained.•Precise approximations in the phase space for this connecting orbit are also obtained.•This higher-order approximation is acquired for the first time in the literature.
论文关键词：Nonlinear time transformation,Takens–Bogdanov bifurcation,Cuspidal loop,Homoclinic orbit
论文评审过程：Received 27 June 2019, Revised 27 December 2019, Accepted 4 January 2020, Available online 21 January 2020, Version of Record 21 January 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125042
