Does synchronization of networks of chaotic maps lead to control?
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.
Zhu
Mingqiang
M
Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA.
Armbruster
Dieter
D
Katzorke
Ines
I
D000465:Algorithms; D000818:Animals; D004058:Diffusion; D016015:Logistic Models; D015233:Models, Statistical; D008962:Models, Theoretical; D009415:Nerve Net; D017711:Nonlinear Dynamics; D009991:Oscillometry