Noisy homoclinic pulse dynamics

Tom Eaves (Lead / Corresponding author), Neil J. Balmforth

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Abstract

The effect of stochastic perturbations on nearly homoclinic pulse trains is considered for three model systems: a Duffing oscillator, the Lorenz-like Shimizu–Morioka model, and a co-dimension-three normal form. Using the Duffing model as an example, it is demonstrated that the main effect of noise does not originate from the neighbourhood of the fixed point, as is commonly assumed, but due to the perturbation of the trajectory outside that region. Singular perturbation theory is used to quantify this noise effect and is applied to construct maps of pulse spacing for the Shimizu–Morioka and normal form models. The dynamics of these stochastic maps is then explored to examine how noise influences the sequence of bifurcations that take place adjacent to homoclinic connections in Lorenz-like and Shilnikov-type flows.
Original languageEnglish
Article number043104
Number of pages11
JournalChaos
Volume26
Early online date13 Apr 2016
DOIs
Publication statusPublished - 2016

Keywords

  • homoclinic bifurcation
  • stochastic bifurcations
  • reduce models

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