NUMERICAL STUDY OF COEXISTING ATTRACTORS FOR THE HÉNON MAP-Reference-Cited by-同舟云学术

NUMERICAL STUDY OF COEXISTING ATTRACTORS FOR THE HÉNON MAP

Published:2013-07 Issue:07 Volume:23 Page:1330025
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

GALIAS ZBIGNIEW¹,TUCKER WARWICK²

Affiliation:

1. Department of Electrical Engineering, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland

2. Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden

Abstract

The question of coexisting attractors for the Hénon map is studied numerically by performing an exhaustive search in the parameter space. As a result, several parameter values for which more than two attractors coexist are found. Using tools from interval analysis, we show rigorously that the attractors exist. In the case of periodic orbits, we verify that they are stable, and thus proper sinks. Regions of existence in parameter space of the found sinks are located using a continuation method; the basins of attraction are found numerically.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127413300255

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