Noisy homoclinic pulse dynamics
Copyright policy )Noisy homoclinic pulse dynamics
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.
- University of British Columbia Canada
- University of Cambridge United Kingdom
- University of Dundee United Kingdom
homoclinic bifurcation, Ordinary differential equations and systems with randomness, Qualitative investigation and simulation of ordinary differential equation models, Nonlinear oscillations and coupled oscillators for ordinary differential equations, stochastic bifurcations, Transformation and reduction of ordinary differential equations and systems, normal forms, reduce models, 510, Singular perturbations of ordinary differential equations
homoclinic bifurcation, Ordinary differential equations and systems with randomness, Qualitative investigation and simulation of ordinary differential equation models, Nonlinear oscillations and coupled oscillators for ordinary differential equations, stochastic bifurcations, Transformation and reduction of ordinary differential equations and systems, normal forms, reduce models, 510, Singular perturbations of ordinary differential equations
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