Homoclinic and Heteroclinic Bifurcations Close to a Twisted Heteroclinic Cycle

Summary, in English

We study the interaction of a transcritical (or saddle-node) bifurcation with a codimension-0/codimension-2 heteroclinic cycle close to (but away from) the local bifurcation point. The study is motivated by numerical observations on the traveling wave ODE of a reaction–diffusion equation. The manifold organization is such that two branches of homoclinic orbits to each fixed point are created when varying the two parameters controlling the codimension-2 loop. It is shown that the homoclinic orbits may become degenerate in an orbit-flip bifurcation. We establish the occurrence of multi-loop homoclinic and heteroclinic orbits in this system. The double-loop homoclinic orbits are shown to bifurcate in an inclination-flip bifurcation, where a Smale's horseshoe is found.

• Författare: Martin Zimmermann; Mario Natiello
• Avdelning/ar: Dynamical systems
• Publiceringsår: 1998
• Språk: Engelska
• Sidor: 359-375
• Publikation/Tidskrift/Serie: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
• Volym: 8
• Issue: 2
• Länkar: http://s0218127498000218.pdf/; http://dx.doi.org/10.1142/S0218127498000218
• Dokumenttyp: Artikel i tidskrift
• Förlag: World Scientific Publishing
• Ämne: Mathematics
• Status: Published
• Forskningsgrupp: Analysis and Dynamics; Dynamical systems
• ISBN/ISSN/Övrigt: ISSN: 0218-1274