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Local bifurcations of a quasiperiodic orbit

Lookup NU author(s): Professor Soumitro Banerjee, Dr Damian Giaouris, Dr Petros Missailidis, Otman Imrayed

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Abstract

We consider the local bifurcations that can occur in a quasiperiodic orbit in a three-dimensional map: (a) a torus doubling resulting in two disjoint loops, (b) a torus doubling resulting in a single closed curve with two loops, (c) the appearance of a third frequency, and (d) the birth of a stable torus and an unstable torus. We analyze these bifurcations in terms of the stability of the point at which the closed invariant curve intersects a "second Poincare section". We show that these bifurcations can be classified depending on where the eigenvalues of this fixed point cross the unit circle.


Publication metadata

Author(s): Banerjee S, Giaouris D, Missailidis P, Imrayed O

Publication type: Article

Publication status: Published

Journal: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Year: 2012

Volume: 22

Issue: 12

Print publication date: 01/12/2012

ISSN (print): 0218-1274

ISSN (electronic): 1793-6551

Publisher: World Scientific Publishing Co. Pte. Ltd.

URL: http://dx.doi.org/10.1142/S0218127412502896

DOI: 10.1142/S0218127412502896


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