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Showing 1 to 8 of 8 for “"Homoclinic orbit"”.
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Stochastic Averaging Correctors for a Noisy Hamiltonian System With Discontinuous Statistics
… a noisy planar Hamiltonian system containing a homoclinic orbit. The noise is assumed to be small and have skewness at the homoclinic orbit. Following Sowers, we center our efforts on a singular perturbations problem in a boundary layer near the homoclinic orbit. At the heart of this analysis is …
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Exploring global dynamics in a low order model of parallel shear flow
… namely LPNS, ensures that we can find homoclinic and heteroclinic connections of limit cycles in the parameter space surrounding the it. We use a matrix-free manifold computation method to find a homoclinic orbit of limit cycles. Finally we will discuss a method to continue the …
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Invariant Manifolds of a Toy Climate Model
… ice ages are caused by variations in the Earth's orbit. However, ice core data shows strong fluctuations in ice volume at a low frequency not significantly present in orbital variations. To understand how this might occur, the dynamics of a two dimensional nonlinear differential equation …
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Mixing enhancement by dual speed rotating stirrer
… the presence of degenerate fixed points and homoclinic/heteroclinic orbits, whose nature varies for different parameter values. By considering an initially concentrated set of marker particles and using the various structures of the phase space in the bifurcation diagram, we produce a complex …
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A Spatial Dynamic Approach to Three-Dimensional Gravity-Capillary Water Waves
… case (b,λ) â C₁. Then, from the existence of the homoclinic orbit connecting to the two-dimensional periodic solution (called generalized solitary wave) for the dominant system, it is obtained that such generalized solitary wave solution persists for the original system by using the perturbation …
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Spinning Black Hole Pairs: Dynamics and Gravitational Waves
… and/or in which they stay on quasi-circular orbits. However, spinning black hole pairs in eccentric orbits are now understood to be astrophysically equally important. These spinning binaries exhibit a range of complicated dynamical behaviors, even in the absence of radiation reaction. Their …
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Optically induced orientational transitions in nematic liquid crystals
… to a state with large reorientation occurs via a homoclinic bifurcation. The homoclinic orbit involved is of the simplest type where a limit cycle collides with a saddle point having one unstable direction. The new state corresponds to a uniform precession of the director, however, with very large …
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Advances in numerical bifurcation software : MatCont
The mathematical background of MatCont, a freely available toolbox, is bifurcation theory which is a field of hard analysis. Bifurcation theory treats dynamical systems from a high-level point of view. In the case of continuous dynamical systems this means that it considers nonlinear differential …