### 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 language | English (US) |
---|---|

Article number | 014101 |

Journal | Chaos |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - 2005 |

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### ASJC Scopus subject areas

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

### Cite this

*Chaos*,

*15*(1), [014101]. https://doi.org/10.1063/1.1839331

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

Research output: Contribution to journal › Article

*Chaos*, vol. 15, no. 1, 014101. https://doi.org/10.1063/1.1839331

}

TY - JOUR

T1 - Does synchronization of networks of chaotic maps lead to control?

AU - Zhu, Mingqiang

AU - Armbruster, Hans

AU - Katzorke, Ines

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=17744366444&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17744366444&partnerID=8YFLogxK

U2 - 10.1063/1.1839331

DO - 10.1063/1.1839331

M3 - Article

C2 - 15836276

AN - SCOPUS:17744366444

VL - 15

JO - Chaos (Woodbury, N.Y.)

JF - Chaos (Woodbury, N.Y.)

SN - 1054-1500

IS - 1

M1 - 014101

ER -