Snakes and isolas in non-reversible conservative systems

DOI10.1080/14689367.2012.691961zbMath1254.35121OpenAlexW2060210713WikidataQ60143873 ScholiaQ60143873MaRDI QIDQ4648497

Björn Sandstede, Yan Cong Xu

Publication date: 9 November 2012

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689367.2012.691961

zbMATH Keywords

bifurcation diagramslocalized pattern

Mathematics Subject Classification ID

Bifurcations in context of PDEs (35B32) Initial value problems for higher-order parabolic equations (35K30) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Semilinear parabolic equations (35K58)

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Uses Software

• AUTO
• AUTO-07P

Cites Work

• Lyapunov-Schmidt reduction for unfolding heteroclinic networks of equilibria and periodic orbits with tangencies
• Snaking of radial solutions of the multi-dimensional Swift-Hohenberg equation: a numerical study
• Exponential asymptotics of localised patterns and snaking bifurcation diagrams
• Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
• Isolas of 2-pulse solutions in homoclinic snaking scenarios
• Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit
• The emergence of a coherent structure for coherent structures: localized states in nonlinear systems
• Nonreversible homoclinic snaking
• Unfolding a Tangent Equilibrium-to-Periodic Heteroclinic Cycle
• Snakes, Ladders, and Isolas of Localized Patterns
• Non-reversible perturbations of homoclinic snaking scenarios
• Spatially localized structures in dissipative systems: open problems
• Lin's method for heteroclinic chains involving periodic orbits