TY  - JOUR
A1  - Amigó, José M.
A1  - Kloeden, Peter E.
A1  - Giménez, Ángel
T1  - Entropy increase in switching systems
T2  - Entropy: an international and interdisciplinary journal of entropy and information studies
N2  - The relation between the complexity of a time-switched dynamics and the complexity of its control sequence depends critically on the concept of a non-autonomous pullback attractor. For instance, the switched dynamics associated with scalar dissipative affine maps has a pullback attractor consisting of singleton component sets. This entails that the complexity of the control sequence and switched dynamics, as quantified by the topological entropy, coincide. In this paper we extend the previous framework to pullback attractors with nontrivial components sets in order to gain further insights in that relation. This calls, in particular, for distinguishing two distinct contributions to the complexity of the switched dynamics. One proceeds from trajectory segments connecting different component sets of the attractor; the other contribution proceeds from trajectory segments within the component sets. We call them “macroscopic” and “microscopic” complexity, respectively, because only the first one can be measured by our analytical tools. As a result of this picture, we obtain sufficient conditions for a switching system to be more complex than its unswitched subsystems, i.e., a complexity analogue of Parrondo’s paradox.
KW  - non-autonomous dynamical systems
KW  - switching systems
KW  - set-valued pullback attractors
KW  - topological entropy
KW  - complexity
Y1  - 2013
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/31440
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-314404
SN  - 1099-4300
N1  - © 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).
VL  - 15
SP  - 2363
EP  - 2383
PB  - MDPI
CY  - Basel
ER  -