Bistability and border-collision bifurcations for a family ofunimodal piecewise smooth maps

Iryna Sushko; Anna Agliari; Laura Gardini

doi:10.3934/dcdsb.2005.5.881

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2005, Volume 5, Issue 3: 881-897. Doi: 10.3934/dcdsb.2005.5.881

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Bistability and border-collision bifurcations for a family of unimodal piecewise smooth maps

1.
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska st., 01601 Kiev
2.
Faculty of Economics, Catholic University, Via Emilia Parmense, 84, 49100 Piacenza
3.
Faculty of Economics, University of Urbino, via Saffi 42, 61029 Urbino (PU)

Received: March 31, 2004

Revised: January 31, 2005

Published: July 2005

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Abstract

This article deals with a two-parameter family of piecewise smooth unimodal maps with one break point. Using superstable cycles and their symbolic representation we describe the structure of the periodicity regions of the 2D bifurcation diagram. Particular attention is paid to the bistability regions corresponding to two coexisting attractors, and to the border-collision bifurcations.

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Mathematics Subject Classification: Primary: 37E05, 37G35; Secondary: 37N30.

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Bistability and border-collision bifurcations for a family of unimodal piecewise smooth maps

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