KCC Analysis of the Normal Form of Typical Bifurcations in One-Dimensional Dynamical Systems: Geometrical Invariants of Saddle-Node, Transcritical, and Pitchfork Bifurcations

DOI10.1142/S0218127417501450zbMath1373.34060OpenAlexW2752337041MaRDI QIDQ5371182

Kazuhito Yamasaki, Takahiro Yajima

Publication date: 25 October 2017

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

Full work available at URL: https://doi.org/10.1142/s0218127417501450

zbMATH Keywords

differential geometrybifurcation theoryJacobi stabilitynonlinear connectionKCC theorydeviation curvature

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Geometric methods in ordinary differential equations (34A26) Bifurcation theory for ordinary differential equations (34C23)

Related Items (8)

Kosambi–Cartan–Chern Stability in the Intermediate Nonequilibrium Region of the Brusselator Model ⋮ Kosambi–Cartan–Chern Analysis of the Nonequilibrium Singular Point in One-Dimensional Elementary Catastrophe ⋮ Qualitative geometric analysis of traveling wave solutions of the modified equal width Burgers equation ⋮ Classification of time-optimal paths under an external force based on Jacobi stability in Finsler space ⋮ Dynamics at infinity and Jacobi stability of trajectories for the Yang-Chen system ⋮ KCC Analysis of a One-Dimensional System During Catastrophic Shift of the Hill Function: Douglas Tensor in the Nonequilibrium Region ⋮ Jacobi Stability Analysis and the Onset of Chaos in a Two-Degree-of-Freedom Mechanical System ⋮ Analysis of Geometric Invariants for Three Types of Bifurcations in 2D Differential Systems

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