TY - JOUR
T1 - Border collision bifurcation curves and their classification in a family of 1D discontinuous maps
AU - Gardini, Laura
AU - Tramontana, Fabio
PY - 2011
Y1 - 2011
N2 - In this paper we consider a one-dimensional piecewise linear discontinuous map in canonical form, which may be used in several physical and engineering applications as well as to model some simple financial markets. We classify three different kinds of possible dynamic behaviors associated with the stable cycles. One regime (i) is the same existing in the continuous case and it is characterized by periodicity regions following the period increment by 1 rule. The second one (ii) is the regime characterized by periodicity regions of period increment higher than 1 (we shall see examples with 2 and 3), and by bistability. The third one (iii) is characterized by infinitely many periodicity regions of stable cycles, which follow the period adding structure, and multistability cannot exist. The analytical equations of the border collision bifurcation curves bounding the regions of existence of stable cycles are determined by using a new approach.
AB - In this paper we consider a one-dimensional piecewise linear discontinuous map in canonical form, which may be used in several physical and engineering applications as well as to model some simple financial markets. We classify three different kinds of possible dynamic behaviors associated with the stable cycles. One regime (i) is the same existing in the continuous case and it is characterized by periodicity regions following the period increment by 1 rule. The second one (ii) is the regime characterized by periodicity regions of period increment higher than 1 (we shall see examples with 2 and 3), and by bistability. The third one (iii) is characterized by infinitely many periodicity regions of stable cycles, which follow the period adding structure, and multistability cannot exist. The analytical equations of the border collision bifurcation curves bounding the regions of existence of stable cycles are determined by using a new approach.
KW - Border-Collision bifurcations
KW - Discontinuous maps
KW - Border-Collision bifurcations
KW - Discontinuous maps
UR - http://hdl.handle.net/10807/67615
U2 - 10.1016/j.chaos.2011.02.001
DO - 10.1016/j.chaos.2011.02.001
M3 - Article
SN - 1873-2887
VL - 44
SP - 248
EP - 259
JO - CHAOS, SOLITONS & FRACTALS
JF - CHAOS, SOLITONS & FRACTALS
ER -