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Nonreversible homoclinic snaking

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2011

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Knobloch, Jürgen
Vielitz, Martin

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https://doi.org/10.1080/14689367.2011.592488
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Dynamical Systems. Taylor & Francis. 2011, 26(3), pp. 335-365. ISSN 1468-9367. eISSN 1468-9375. Available under: doi: 10.1080/14689367.2011.592488

Zusammenfassung

Homoclinic snaking refers to the sinusoidal ‘snaking’ continuation curve of homoclinic orbits near a heteroclinic cycle connecting an equilibrium E and a periodic orbit P. Along this curve the homoclinic orbit performs more windings about the periodic orbit. Typically, this behaviour appears in reversible Hamiltonian systems. Here we discuss this phenomenon in systems without any particular structure. We give a rigorous analytical verification of homoclinic snaking under certain assumptions on the behaviour of the stable and unstable manifolds of E and P. We show how the snaking behaviour depends on the signs of the Floquet multipliers of P. Further we present a nonsnaking scenario. Finally, we show numerically that these assumptions are fulfilled in a model equation.

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global bifurcation, homoclinic snaking, heteroclinic cycle

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ISO 690KNOBLOCH, Jürgen, Thorsten RIESS, Martin VIELITZ, 2011. Nonreversible homoclinic snaking. In: Dynamical Systems. Taylor & Francis. 2011, 26(3), pp. 335-365. ISSN 1468-9367. eISSN 1468-9375. Available under: doi: 10.1080/14689367.2011.592488
BibTex
@article{Knobloch2011-09Nonre-51314,
  year={2011},
  doi={10.1080/14689367.2011.592488},
  title={Nonreversible homoclinic snaking},
  number={3},
  volume={26},
  issn={1468-9367},
  journal={Dynamical Systems},
  pages={335--365},
  author={Knobloch, Jürgen and Rieß, Thorsten and Vielitz, Martin}
}
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