SLOW INVARIANT MANIFOLDS AS CURVATURE OF THE FLOW OF DYNAMICAL SYSTEMS

DOI10.1142/S0218127408022457zbMath1165.37314arXiv1408.1712MaRDI QIDQ5322583

Bruno Rossetto, Leon O. Chua, Jean-Marc Ginoux

Publication date: 21 July 2009

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

Full work available at URL: https://arxiv.org/abs/1408.1712

zbMATH Keywords

torsioncurvaturedifferential geometryDarboux invariantGram--Schmidt algorithm

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Qualitative investigation and simulation of ordinary differential equation models (34C60) Invariant manifold theory for dynamical systems (37D10) Curves in Euclidean and related spaces (53A04) Invariant manifolds for ordinary differential equations (34C45)

Related Items (14)

On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature ⋮ An Invariant-Manifold Approach to Lumping ⋮ TWO-DIMENSIONAL DYNAMICAL SYSTEMS WITH PERIODIC COEFFICIENTS ⋮ A Lin's method approach for detecting all canard orbits arising from a folded node ⋮ A New Frame for an Old (Phase) Portrait: Finding Rivers and Other Flow Features in the Plane ⋮ Towards Differential Geometric Characterization of Slow Invariant Manifolds in Extended Phase Space: Sectional Curvature and Flow Invariance ⋮ Extending the zero-derivative principle for slow-fast dynamical systems ⋮ The slow invariant manifold of the Lorenz-Krishnamurthy model ⋮ Inflection, canards and folded singularities in excitable systems: application to a 3D FitzHugh-Nagumo model ⋮ On unifying concepts for trajectory-based slow invariant attracting manifold computation in kinetic multiscale models ⋮ Unbounded dynamics in dissipative flows: Rössler model ⋮ CANARDS FROM CHUA'S CIRCUIT ⋮ Slow Invariant Manifolds of Slow–Fast Dynamical Systems ⋮ Flow curvature manifold and energy of generalized Liénard systems

Cites Work

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• Multiplicity of invariant algebraic curves in polynomial vector fields
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• The double scroll family
• Nonlinear periodic convection in double-diffusive systems
• HYPERCHAOS IN A MODIFIED CANONICAL CHUA'S CIRCUIT
• A GALLERY OF ATTRACTORS FROM SMOOTH CHUA'S EQUATION
• Slow-Fast Autonomous Dynamical Systems
• DIFFERENTIAL GEOMETRY AND MECHANICS: APPLICATIONS TO CHAOTIC DYNAMICAL SYSTEMS
• Higher Curvatures of Curves in Euclidean Space

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