Does synchronization of networks of chaotic maps lead to control?

Mingqiang Zhu, Hans Armbruster, Ines Katzorke

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider networks of chaotic maps with different network topologies. In each case, they are coupled in such a way as to generate synchronized chaotic solutions. By using the methods of control of chaos we are controlling a single map into a predetermined trajectory. We analyze the reaction of the network to such a control. Specifically we show that a line of one-dimensional logistic maps that are unidirectionally coupled can be controlled from the first oscillator whereas a ring of diffusively coupled maps cannot be controlled for more than 5 maps. We show that rings with more elements can be controlled if every third map is controlled. The dependence of unidirectionally coupled maps on noise is studied. The noise level leads to a finite synchronization lengths for which maps can be controlled by a single location. A two-dimensional lattice is also studied.

Original languageEnglish (US)
Article number014101
JournalChaos
Volume15
Issue number1
DOIs
StatePublished - 2005

Fingerprint

Chaotic Map
synchronism
Synchronization
Coupled Maps
Ring
Control of Chaos
Logistic map
Network Topology
Trajectory
Line
rings
logistics
Chaos theory
chaos
Logistics
topology
Trajectories
oscillators
Topology
trajectories

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Does synchronization of networks of chaotic maps lead to control? / Zhu, Mingqiang; Armbruster, Hans; Katzorke, Ines.

In: Chaos, Vol. 15, No. 1, 014101, 2005.

Research output: Contribution to journalArticle

Zhu, Mingqiang ; Armbruster, Hans ; Katzorke, Ines. / Does synchronization of networks of chaotic maps lead to control?. In: Chaos. 2005 ; Vol. 15, No. 1.
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