Homoclinic Bifurcations

Andrew Fowler () and Mark McGuinness
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Andrew Fowler: University of Limerick, MACSI
Mark McGuinness: Victoria University of Wellington, School of Mathematics and Statistics

Chapter Chapter 4 in Chaos, 2019, pp 99-142 from Springer

Abstract: Abstract Homoclinic bifurcation theory is discussed, beginning with the Lorenz equations as an example, and the corresponding two-dimensional Poincaré map and its one-dimensional approximation are derived. Symbolic dynamics and the Smale horseshoe are described, and then Shilnikov bifurcations for saddle-focus homoclinic bifurcations are analysed. The final section generalises the results to n-dimensional flows, and mentions the corresponding results for infinite-dimensional (partial differential equation) flows, without detail. The possible relation to fluid turbulence is mentioned.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-32538-1_4

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DOI: 10.1007/978-3-030-32538-1_4

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