CONTINUATION OF CONNECTING ORBITS IN 3D-ODEs (II) : CYCLE-TO-CYCLE CONNECTIONS

DOI10.1142/S0218127409022804zbMath1170.37339arXiv0804.0179OpenAlexW2950197822MaRDI QIDQ3398168

Eusebius J. Doedel, George A. K. Van Voorn, Yuri A. Kuznetsov, Bob W. Kooi

Publication date: 25 September 2009

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

Full work available at URL: https://arxiv.org/abs/0804.0179

zbMATH Keywords

boundary value problemsglobal bifurcationsprojection boundary conditionscycle-to-cycle connections

Mathematics Subject Classification ID

Qualitative theory for ordinary differential equations (34C99) Approximation methods and numerical treatment of dynamical systems (37M99) Numerical problems in dynamical systems (65P99)

Related Items (13)

Parameterization of invariant manifolds for periodic orbits. II: A posteriori analysis and computer assisted error bounds ⋮ Determining the global manifold structure of a continuous-time heterodimensional cycle ⋮ Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits ⋮ Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations ⋮ Validated numerics for continuation and bifurcation of connecting orbits of maps ⋮ Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem ⋮ Continuation and Bifurcation of Grain Boundaries in the Swift--Hohenberg Equation ⋮ Analysis of the relative dynamics of a charged spacecraft moving under the influence of a magnetic field ⋮ The onset of transient turbulence in minimal plane Couette flow ⋮ Homoclinic dynamics in a spatial restricted four-body problem: blue skies into Smale horseshoes for vertical Lyapunov families ⋮ Ecological consequences of global bifurcations in some food chain models ⋮ BIFURCATION STRUCTURES IN A MODEL OF A CO₂ LASER WITH A FAST SATURABLE ABSORBER ⋮ Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications

Cites Work

• Unnamed Item
• Forest-pest interaction dynamics: The simplest mathematical models
• Homoclinic and heteroclinic orbits to a cycle in a tri-trophic food chain
• Chaos in three species food chains
• On locating connecting orbits
• Erratum: Point-to-periodic and periodic-to-periodic connections
• Point-to-periodic and periodic-to-periodic connections
• Bifurcation structure of a three-species food chain model
• Remarks on food chain dynamics
• Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect
• Belyakov Homoclinic Bifurcations in a Tritrophic Food Chain Model
• CONTINUATION OF CONNECTING ORBITS IN 3D-ODEs (I): POINT-TO-CYCLE CONNECTIONS
• NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
• A NUMERICAL TOOLBOX FOR HOMOCLINIC BIFURCATION ANALYSIS
• Computing Connecting Orbits via an Improved Algorithm for Continuing Invariant Subspaces
• ON A POINCARÉ-BIRKHOFF PROBLEM
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I
• Multiple attractors and boundary crises in a tri-trophic food chain
• Numerical approximation of connecting orbits with asymptotic rate

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