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Does synchronization of networks of chaotic maps lead to control? Mingqiang Zhu and Dieter Armbruster
 

Summary: Does synchronization of networks of chaotic maps lead to control?
Mingqiang Zhu and Dieter Armbruster
Department of Mathematics, Arizona State University, Tempe, Arizona 85287
Ines Katzorke
Department of Physics, University of Potsdam, Germany
Received 11 May 2004; accepted 4 November 2004; published online 13 January 2005
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 unidi-
rectionally 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. 2005 American Institute of Physics. DOI: 10.1063/1.1839331
It is well known that strongly coupled chaotic oscillators
may synchronize and oscillate collectively in a chaotic
way. Additionally, due to the inherent instability of cha-
otic systems, we can steer trajectories in a desired direc-

  

Source: Armbruster, Dieter - Department of Mathematics and Statistics, Arizona State University

 

Collections: Mathematics