Showcase of Blue Sky Catastrophes-Reference-Cited by-同舟云学术

Showcase of Blue Sky Catastrophes

Published:2014-08 Issue:08 Volume:24 Page:1440003
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Shilnikov Leonid Pavlovich¹,Shilnikov Andrey L.²³,Turaev Dmitry V.⁴

Affiliation:

1. Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, 603005, Russia

2. Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta 30303, USA

3. Department of Computational Mathematics and Cybernetics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950, Russia

4. Department of Mathematics, Imperial College London, SW7 2AZ, UK

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127414400033

Reference36 articles.

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2. The ring principle in problems of interaction between two self-oscillating systems

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