GLOBAL BIFURCATIONS OF CLOSED INVARIANT CURVES IN TWO-DIMENSIONAL MAPS: A COMPUTER ASSISTED STUDY-Reference-Cited by-同舟云学术

GLOBAL BIFURCATIONS OF CLOSED INVARIANT CURVES IN TWO-DIMENSIONAL MAPS: A COMPUTER ASSISTED STUDY

Published:2005-04 Issue:04 Volume:15 Page:1285-1328
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

AGLIARI ANNA¹,BISCHI GIAN-ITALO²,DIECI ROBERTO³,GARDINI LAURA²

Affiliation:

1. Istituto di Econometria e Matematica AEFA, Catholic University of Milano, Italy

2. Istituto di Scienze Economiche, University of Urbino, Italy

3. Dipartimento di Matematica per le Scienze Economiche e Sociali, University of Bologna, Italy

Abstract

In this paper we describe some sequences of global bifurcations involving attracting and repelling closed invariant curves of two-dimensional maps that have a fixed point which may lose stability both via a supercritical Neimark bifurcation and a supercritical pitchfork or flip bifurcation. These bifurcations, characterized by the creation of heteroclinic and homoclinic connections or homoclinic tangles, are first described through qualitative phase diagrams and then by several numerical examples. Similar bifurcation phenomena can also be observed when the parameters in a two-dimensional parameter plane cross through many overlapping Arnold's tongues.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127405012685

Reference24 articles.

1. Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer-assisted study

2. Elementary Symbolic Dynamics and Chaos in Dissipative Systems

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