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August  2005, 5(3): 881-897. doi: 10.3934/dcdsb.2005.5.881

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

Iryna Sushko 1, , Anna Agliari 2, and  Laura Gardini 3,

1. 

Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska st., 01601 Kiev, Ukraine
2. 

Faculty of Economics, Catholic University, Via Emilia Parmense, 84, 49100 Piacenza, Italy
3. 

Faculty of Economics, University of Urbino, via Saffi 42, 61029 Urbino (PU), Italy

Received  April 2004 Revised  February 2005 Published  May 2005

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.
Keywords: bistability., Unimodal piecewise smooth map, bifurcation diagram, border-collision bifurcation.
Mathematics Subject Classification: Primary: 37E05, 37G35; Secondary: 37N3.
Citation: Iryna Sushko, Anna Agliari, Laura Gardini. Bistability and border-collision bifurcations for a family of unimodal piecewise smooth maps. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 881-897. doi: 10.3934/dcdsb.2005.5.881
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