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- W4313137020 abstract "<abstract><p>We consider an autonomous ordinary differential equation that admits a heteroclinic loop. The unperturbed heteroclinic loop consists of two degenerate heteroclinic orbits $ gamma_1 $ and $ gamma_2 $. We assume the variational equation along the degenerate heteroclinic orbit $ gamma_i $ has $ {d_i}left({{d_i} > 1, i = 1, 2} right) $ linearly independent bounded solutions. Moreover, the splitting indices of the unperturbed heteroclinic orbits are $ s $ and $ -s $ $ (sgeq 0) $, respectively. In this paper, we study the persistence of the heteroclinic loop under periodic perturbation. Using the method of Lyapunov-Schmidt reduction and exponential dichotomies, we obtained the bifurcation function, which is defined from $ mathbb{R}^{d_1+d_2+2} $ to $ mathbb{R}^{d_1+d_2} $. Under some conditions, the perturbed system can have a heteroclinic loop near the unperturbed heteroclinic loop.</p></abstract>" @default.
- W4313137020 created "2023-01-06" @default.
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- W4313137020 date "2023-01-01" @default.
- W4313137020 modified "2023-09-26" @default.
- W4313137020 title "Persistence of the heteroclinic loop under periodic perturbation" @default.
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- W4313137020 doi "https://doi.org/10.3934/era.2023054" @default.
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