Examples of non-degenerate and degenerate cuspidal loops in planar systems

DOI10.1080/026811199282038zbMath0930.34031OpenAlexW2330774357MaRDI QIDQ4257742

Alejandro J. Rodríguez-Luis, Emilio Freire, Luis Pizarro

Publication date: 31 August 1999

Published in: Dynamics and Stability of Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/026811199282038

zbMATH Keywords

bifurcationshomoclinic orbitplanar systemsDulac mapseparatricescodimension-five Bogdanov-Takens bifurcationcuspidal loops

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (2)

Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system ⋮ Analytical approximation of cuspidal loops using a nonlinear time transformation method

Uses Software

• Unnamed Item
• DSTool
• HomCont

Cites Work

• Unnamed Item
• On a four parameter family of planar vector fields
• Hysteresis, oscillations, and pattern formation in realistic immobilized enzyme systems
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• The Saddle-Node Separatrix-Loop Bifurcation
• Bifurcations of cuspidal loops
• Numerical continuation of degenerate homoclinic orbits in planar systems
• NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
• A NUMERICAL TOOLBOX FOR HOMOCLINIC BIFURCATION ANALYSIS

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