Showcase of blue sky catastrophes

Leonid Pavlovich Shilnikov; Andrey L. Shilnikov; Dmitry V. Turaev

doi:10.1142/S0218127414400033

Showcase of blue sky catastrophes

Leonid Pavlovich Shilnikov, Andrey L. Shilnikov, Dmitry V. Turaev

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

Let a system of differential equations possess a saddle periodic orbit such that every orbit in its unstable manifold is homoclinic, i.e. the unstable manifold is a subset of the (global) stable manifold. We study several bifurcation cases of the breakdown of such a homoclinic connection that causes the blue sky catastrophe, as well as the onset of complex dynamics. The birth of an invariant torus and a Klein bottle is also described.

Original language	English
Article number	1440003
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	24
Issue number	8
DOIs	https://doi.org/10.1142/S0218127414400033
State	Published - 1 Jan 2014
Externally published	Yes

Keywords

Codimension-one
blue sky catastrophe
homoclinic bifurcations

ASJC Scopus subject areas

Modeling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

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10.1142/S0218127414400033

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title = "Showcase of blue sky catastrophes",

abstract = "Let a system of differential equations possess a saddle periodic orbit such that every orbit in its unstable manifold is homoclinic, i.e. the unstable manifold is a subset of the (global) stable manifold. We study several bifurcation cases of the breakdown of such a homoclinic connection that causes the blue sky catastrophe, as well as the onset of complex dynamics. The birth of an invariant torus and a Klein bottle is also described.",

keywords = "Codimension-one, blue sky catastrophe, homoclinic bifurcations",

author = "Shilnikov, {Leonid Pavlovich} and Shilnikov, {Andrey L.} and Turaev, {Dmitry V.}",

note = "Funding Information: This work was in part supported by NSF DMS-1009591 and RFFI 11-01-00001 (to A. Shilnikov), and the Royal Society Grant “Homoclinic bifurcations” (to D. Turaev).",

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T1 - Showcase of blue sky catastrophes

AU - Shilnikov, Leonid Pavlovich

AU - Shilnikov, Andrey L.

AU - Turaev, Dmitry V.

N1 - Funding Information: This work was in part supported by NSF DMS-1009591 and RFFI 11-01-00001 (to A. Shilnikov), and the Royal Society Grant “Homoclinic bifurcations” (to D. Turaev).

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Let a system of differential equations possess a saddle periodic orbit such that every orbit in its unstable manifold is homoclinic, i.e. the unstable manifold is a subset of the (global) stable manifold. We study several bifurcation cases of the breakdown of such a homoclinic connection that causes the blue sky catastrophe, as well as the onset of complex dynamics. The birth of an invariant torus and a Klein bottle is also described.

AB - Let a system of differential equations possess a saddle periodic orbit such that every orbit in its unstable manifold is homoclinic, i.e. the unstable manifold is a subset of the (global) stable manifold. We study several bifurcation cases of the breakdown of such a homoclinic connection that causes the blue sky catastrophe, as well as the onset of complex dynamics. The birth of an invariant torus and a Klein bottle is also described.

KW - Codimension-one

KW - blue sky catastrophe

KW - homoclinic bifurcations

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U2 - 10.1142/S0218127414400033

DO - 10.1142/S0218127414400033

M3 - Article

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SN - 0218-1274

VL - 24

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 8

M1 - 1440003

ER -

Showcase of blue sky catastrophes

Abstract

Keywords

ASJC Scopus subject areas

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