NUMERICAL STUDY OF COEXISTING ATTRACTORS FOR THE HÉNON MAP

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)

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