TY - JOUR
T1 - Adaptation to the edge of chaos in the self-adjusting logistic map
AU - Melby, Paul
AU - Kaidel, Jörg
AU - Weber, Nicholas
AU - Hübler, Alfred
PY - 2000
Y1 - 2000
N2 - Self-adjusting, or adaptive, systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these parameters is governed by a low-pass filtered feedback from the dynamical variables of the system. We apply this model to the logistic map and examine the behavior of the control parameter. We find that the parameter leaves the chaotic regime. We observe a high probability of finding the parameter at the boundary between periodicity and chaos. We therefore find that this system exhibits adaptation to the edge of chaos.
AB - Self-adjusting, or adaptive, systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these parameters is governed by a low-pass filtered feedback from the dynamical variables of the system. We apply this model to the logistic map and examine the behavior of the control parameter. We find that the parameter leaves the chaotic regime. We observe a high probability of finding the parameter at the boundary between periodicity and chaos. We therefore find that this system exhibits adaptation to the edge of chaos.
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U2 - 10.1103/PhysRevLett.84.5991
DO - 10.1103/PhysRevLett.84.5991
M3 - Article
C2 - 10991106
AN - SCOPUS:0034717369
SN - 0031-9007
VL - 84
SP - 5991
EP - 5993
JO - Physical review letters
JF - Physical review letters
IS - 26
ER -