Homoclinic snaking near a heteroclinic cycle in reversible systems
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Publication:2485290
DOI10.1016/j.physd.2005.04.018zbMath1084.34049OpenAlexW2049546479MaRDI QIDQ2485290
Jürgen Knobloch, Thomas Wagenknecht
Publication date: 4 August 2005
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: http://eprints.maths.manchester.ac.uk/663/1/snaking_prep.pdf
Bifurcation theory for ordinary differential equations (34C23) Asymptotic expansions of solutions to ordinary differential equations (34E05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)
Related Items (19)
CODIMENSION 3 HETEROCLINIC BIFURCATIONS WITH ORBIT AND INCLINATION FLIPS IN REVERSIBLE SYSTEMS ⋮ The twisting bifurcations of double homoclinic loops with resonant eigenvalues ⋮ Defect-mediated snaking: a new growth mechanism for localized structures ⋮ Homoclinic flip bifurcation with a nonhyperbolic equilibrium ⋮ On the existence of bifocal heteroclinic cycles in a class of four-dimensional piecewise affine systems ⋮ Two-dimensional localized structures in harmonically forced oscillatory systems ⋮ Organization of Spatially Localized Structures near a Codimension-Three Cusp-Turing Bifurcation ⋮ Homoclinic flip bifurcations accompanied by transcritical bifurcation ⋮ Localized Turing patterns in nonlinear optical cavities ⋮ Nonlocal Raman response in Kerr resonators: Moving temporal localized structures and bifurcation structure ⋮ Effect of driving on coarsening dynamics in phase-separating systems ⋮ Snakes and ladders: localized states in the Swift-Hohenberg equation ⋮ From steady solutions to chaotic flows in a Rayleigh-Bénard problem at moderate Rayleigh numbers ⋮ Exponential asymptotics of localised patterns and snaking bifurcation diagrams ⋮ Symmetric periodic orbits near a heteroclinic loop in \(\mathbb R^3\) formed by two singular points, a semistable periodic orbit and their invariant manifolds ⋮ Homoclinic snaking: Structure and stability ⋮ Nonreversible homoclinic snaking ⋮ Infinitely many multi-pulses near a bifocal cycle ⋮ Snakes and ladders in an inhomogeneous neural field model
Uses Software
Cites Work
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