Cascades of Global Bifurcations and Chaos near a Homoclinic Flip Bifurcation: A Case Study

DOI10.1137/17M1149675zbMath1408.37087OpenAlexW2902854979WikidataQ128992608 ScholiaQ128992608MaRDI QIDQ4562427

Bernd Krauskopf, Andrus Giraldo, Hinke M. Osinga

Publication date: 20 December 2018

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

Full work available at URL: https://doi.org/10.1137/17m1149675

zbMATH Keywords

chaotic attractorinclination fliphomoclinic tangencieshomoclinic and heteroclinic bifurcationsglobal invariant manifoldssaddle periodic orbits

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Invariant manifolds for ordinary differential equations (34C45) Computational methods for bifurcation problems in dynamical systems (37M20) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (7)

Rate-Induced Tipping in Heterogeneous Reaction-Diffusion Systems: An Invariant Manifold Framework and Geographically Shifting Ecosystems ⋮ New insights on non-integrability and dynamics in a simple quadratic differential system ⋮ 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 ⋮ Study of a simple 3D quadratic system with homoclinic flip bifurcations of inward twist case \(\mathbf{C}_{\mathbf{in}}\) ⋮ Compactification for asymptotically autonomous dynamical systems: theory, applications and invariant manifolds ⋮ 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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