Homoclinic and Heteroclinic Bifurcations Close to a Twisted Heteroclinic Cycle

DOI10.1142/S0218127498000218zbMath0933.37054MaRDI QIDQ4936194

Mario A. Natiello, Martín G. Zimmermann

Publication date: 24 January 2000

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

zbMATH Keywords

fixed pointreaction-diffusion equationhomoclinic orbitstraveling waveSmale's horseshoeinclination-flip bifurcationmulti-loop homoclinictranscritical or saddle-node bifurcation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Bifurcation theory for ordinary differential equations (34C23) Bifurcations in context of PDEs (35B32) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (7)

Analysis of the T-point-Hopf bifurcation in the Lorenz system ⋮ Dynamics Near the Heterodimensional Cycles with Nonhyperbolic Equilibrium ⋮ Numerical bifurcation and stability analysis of solitary pulses in an excitable reaction-diffusion medium ⋮ Accumulations of \(T\)-points in a model for solitary pulses in an excitable reaction-diffusion medium ⋮ DYNAMICS OF THREE COUPLED EXCITABLE CELLS WITH D₃ SYMMETRY ⋮ RESONANCE STRUCTURE IN A WEAKLY DETUNED LASER WITH INJECTED SIGNAL ⋮ The stability of traveling calcium pulses in a pancreatic acinar cell

Cites Work

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• Propagation Phenomena in a Bistable Reaction-Diffusion System
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• The Existence of Infinitely Many Traveling Front and Back Waves in the FitzHugh–Nagumo Equations
• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit
• NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS

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