COMPUTING TWO-DIMENSIONAL GLOBAL INVARIANT MANIFOLDS IN SLOW–FAST SYSTEMS

DOI10.1142/S0218127407017562zbMath1140.37365OpenAlexW2166634832WikidataQ114476431 ScholiaQ114476431MaRDI QIDQ3499158

Bernd Krauskopf, J. P. England, Hinke M. Osinga

Publication date: 28 May 2008

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127407017562

zbMATH Keywords

boundary value problemsLorenz modelstable and unstable manifoldsslow-fast systemsGlobalizeBVP algorithmsomatotroph cell model

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Dynamical systems in biology (37N25) Symmetries, invariants of ordinary differential equations (34C14) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Invariant manifold theory for dynamical systems (37D10) Approximation methods and numerical treatment of dynamical systems (37M99) Numerical problems in dynamical systems (65P99)

Related Items (7)

Stability of the equilibria of a dynamic system modeling stem cell transplantation ⋮ An adaptive method for computing invariant manifolds in non-autonomous, three-dimensional dynamical systems ⋮ A Lin's method approach for detecting all canard orbits arising from a folded node ⋮ Resetting behavior in a model of bursting in secretory pituitary cells: distinguishing plateaus from pseudo-plateaus ⋮ Characterizing two-timescale nonlinear dynamics using finite-time Lyapunov exponents and subspaces ⋮ Global invariant manifolds near a Shilnikov homoclinic bifurcation ⋮ Visualizing global manifolds during the transition to chaos in the Lorenz system

Cites Work

• Computing Geodesic Level Sets on Global (Un)stable Manifolds of Vector Fields
• Two-dimensional global manifolds of vector fields
• Deterministic Nonperiodic Flow
• SOME RESULTS ON CHUA'S EQUATION NEAR A TRIPLE-ZERO LINEAR DEGENERACY
• A GALLERY OF ATTRACTORS FROM SMOOTH CHUA'S EQUATION
• A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS
• Computing One-Dimensional Global Manifolds of Poincaré Maps by Continuation

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