Saddle Invariant Objects and Their Global Manifolds in a Neighborhood of a Homoclinic Flip Bifurcation of Case B

DOI10.1137/16M1097419zbMath1385.37028MaRDI QIDQ5739156

Bernd Krauskopf, Andrus Giraldo, Hinke M. Osinga

Publication date: 2 June 2017

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

periodic orbitsorbit flipPoincaré compactificationglobal invariant manifoldhomoclinic and heteroclinic bifurcation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Invariant manifold theory for dynamical systems (37D10) Computational methods for bifurcation problems in dynamical systems (37M20) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Bifurcations connected with nontransversal intersection in dynamical systems (37G25) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (9)

A Lin's method approach for detecting all canard orbits arising from a folded node ⋮ Cascades of Global Bifurcations and Chaos near a Homoclinic Flip Bifurcation: A Case Study ⋮ Rate-Induced Tipping in Heterogeneous Reaction-Diffusion Systems: An Invariant Manifold Framework and Geographically Shifting Ecosystems ⋮ Computing connecting orbits to infinity associated with a homoclinic flip bifurcation ⋮ Pulse-adding of temporal dissipative solitons: resonant homoclinic points and the orbit flip of case B with delay ⋮ Finding First Foliation Tangencies in the Lorenz System ⋮ Study of a simple 3D quadratic system with homoclinic flip bifurcations of inward twist case \(\mathbf{C}_{\mathbf{in}}\) ⋮ Saddle slow manifolds and canard orbits in \(\mathbb{R}^{4}\) and application to the full Hodgkin-Huxley model ⋮ Chaotic switching in driven-dissipative Bose-Hubbard dimers: when a flip bifurcation meets a T-point in \(\mathbb{R}^4 \)

Uses Software

• AUTO
• AUTO-07P
• HomCont

Cites Work

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