Publication

Chaotic synchronization of 2-D maps via information transmission

Martin Hasler
2001
Conference Papers

Abstract

The master-slave synchronization of two chaotic systems that interact over a noisy channel is analyzed from an information theoretic point of view. It is argued that arbitrarily precise synchronization, in the sense of the mean square synchronization error, is possible if the channel capacity is higher than the information production rate of the master system. Thus, even with considerable channel noise, very precise synchronization is possible. This is in contrast to the intuitive idea that synchronization necessarily degrades with increasing noise in the channel. A concrete way to achieve this is demonstrated for the Lozi map.

Official source

https://infoscience.epfl.ch/entities/publication/0250d094-f3bf-47ae-85cd-2bd2de93dcc9

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Martin Hasler
2001
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/0250d094-f3bf-47ae-85cd-2bd2de93dcc9

About this result

Related concepts (32)

Synchronization

Synchronization is the coordination of events to operate a system in unison. For example, the conductor of an orchestra keeps the orchestra synchronized or in time. Systems that operate with all parts in synchrony are said to be synchronous or in sync—and those that are not are asynchronous. Today, time synchronization can occur between systems around the world through satellite navigation signals and other time and frequency transfer techniques. Time-keeping and synchronization of clocks is a critical problem in long-distance ocean navigation.

Information theory

Information theory is the mathematical study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering. A key measure in information theory is entropy.

Noisy-channel coding theorem

In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel. This result was presented by Claude Shannon in 1948 and was based in part on earlier work and ideas of Harry Nyquist and Ralph Hartley.

Related publications (32)

Chaotic synchronization of 2-D maps via information transmission

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Noisy Gradient Descent in Machine Learning: generalization, games, and sampling

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