Dynamical Systems with a Codimension-One Invariant Manifold: The Unfoldings and Its Bifurcations

DOI10.1142/S0218127415500911zbMath1317.34076OpenAlexW2203977075MaRDI QIDQ5499900

Kie van Ivanky Saputra

Publication date: 5 August 2015

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

Full work available at URL: https://doi.org/10.1142/s0218127415500911

zbMATH Keywords

transcritical bifurcationinvariant manifoldcodimension-three Bogdanov-Takens bifurcationsaddle Hopf bifurcation

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23) Invariant manifolds for ordinary differential equations (34C45)

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Cites Work

• Unnamed Item
• The saddle-node-transcritical bifurcation in a population model with constant rate harvesting
• Time-reversal symmetry in dynamical systems: a survey
• Elements of applied bifurcation theory.
• Widely separated frequencies in coupled oscillators with energy-preserving quadratic nonlinearity
• The dynamics of two diffusively coupled predator--prey populations.
• Singularities of vector fields
• An energy-momentum map for the time-reversal symmetric 1:1 resonance with \(\mathbb Z_2{\times}\mathbb Z_2\) symmetry
• Symmetric spaces and Lie triple systems in numerical analysis of differential equations
• Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in \(\mathbb R^3\)
• Symmetry and Resonance in Hamiltonian Systems
• A three-dimensional singularly perturbed conservative system with symmetry breaking
• Bifurcation to Quasi-Periodic Tori in the Interaction of Steady State and Hopf Bifurcations
• Bifurcation Analysis of a Mathematical Model for Malaria Transmission
• Chaos and strange attractors in coupled oscillators with energy-preserving nonlinearity
• An integrating factor matrix method to find first integrals
• Reversing symmetries in dynamical systems
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Multiparametric Bifurcation Analysis of a Basic Two-Stage Population Model
• PRACTICAL COMPUTATION OF NORMAL FORMS ON CENTER MANIFOLDS AT DEGENERATE BOGDANOV–TAKENS BIFURCATIONS

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