A NOTE ON THE TRIPLE-ZERO LINEAR DEGENERACY: NORMAL FORMS, DYNAMICAL AND BIFURCATION BEHAVIORS OF AN UNFOLDING-Reference-Cited by-同舟云学术

A NOTE ON THE TRIPLE-ZERO LINEAR DEGENERACY: NORMAL FORMS, DYNAMICAL AND BIFURCATION BEHAVIORS OF AN UNFOLDING

Published:2002-12 Issue:12 Volume:12 Page:2799-2820
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

FREIRE E.¹,GAMERO E.¹,RODRÍGUEZ-LUIS A. J.¹,ALGABA A.²

Affiliation:

1. Department of Applied Mathematics II, E. S. I., University Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain

2. Department of Mathematics, E. P. S., University Huelva, Crta. Palos-Huelva s/n, 21819 La Rábida, Huelva, Spain

Abstract

This paper is devoted to the analysis of bifurcations in a three-parameter unfolding of a linear degeneracy corresponding to a triple-zero eigenvalue. We carry out the study of codimension-two local bifurcations of equilibria (Takens–Bogdanov and Hopf-zero) and show that they are nondegenerate. This allows to put in evidence the presence of several kinds of bifurcations of periodic orbits (secondary Hopf,…) and of global phenomena (homoclinic, heteroclinic). The results obtained are applied in the study of the Rössler equation.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127402006175

Reference22 articles.

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3. Methods of Bifurcation Theory

4. Nilpotent normal forms and representation theory of 𝑠𝑙(2,𝑅)

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