Successive homoclinic tangencies to a limit cycle

DOI10.1016/0167-2789(95)00211-1zbMath0886.34028OpenAlexW2107606441MaRDI QIDQ1903312

P. Hirschberg, Carlo R. Laing

Publication date: 28 November 1995

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(95)00211-1

zbMATH Keywords

periodic orbitsaddle-node bifurcationsperturbed degenerate homoclinic connection

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23)

Related Items (11)

Unfolding homoclinic connections formed by corner intersections in piecewise-smooth maps ⋮ Homoclinic and heteroclinic orbits underlying the post-buckling of axially-compressed cylindrical shells ⋮ Global bifurcations in a laser with injected signal: Beyond Adler’s approximation ⋮ CLOSED CURVES OF GLOBAL BIFURCATIONS IN CHUA'S EQUATION: A MECHANISM FOR THEIR FORMATION ⋮ Subsumed Homoclinic Connections and Infinitely Many Coexisting Attractors in Piecewise-Linear Maps ⋮ Complex oscillations and waves of calcium in pancreatic acinar cells ⋮ Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions ⋮ The non-transverse Shil'nikov-Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies ⋮ Unfolding Codimension-Two Subsumed Homoclinic Connections in Two-Dimensional Piecewise-Linear Maps ⋮ Bifurcation sequences in the interaction of resonances in a model deriving from nonlinear rotordynamics: The zipper ⋮ Isolas, cusps and global bifurcations in an electronic oscillator

Uses Software

• AUTO
• AUTO-86

Cites Work

• Unnamed Item
• Local and global behavior near homoclinic orbits
• An example of bifurcation to homoclinic orbits
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Global bifurcations and chaos. Analytical methods
• Shilnikov-Hopf bifurcation
• Local birth of homoclinic chaos
• Merging of resonance tongues
• Repeated Resonance and Homoclinic Bifurcation in a Periodically Forced Family of Oscillators
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I

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