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Koronovskii A. A. The dynamics of the one-dimensional chain of logistic maps with the unidirectional threshold coupling. Izvestiya VUZ. Applied Nonlinear Dynamics, 1996, vol. 4, iss. 4, pp. 122-129.

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Russian
Heading: 
Autowaves. Self-organization
Article type: 
Article
UDC: 
517.9

The dynamics of the one-dimensional chain of logistic maps with the unidirectional threshold coupling

Autors: 
Koronovskii Aleksei Aleksandrovich, Saratov State University
Abstract: 

This article deals with the behaviour of the one-dimensional (semi-infinite or ring-shaped) chain of logistic maps connected with each other by the unidirectional threshold coupling. This type of coupling is radically new and its influence upon the chain processes results in the new type of dynamics that is unusual for chains of logistic maps with traditional types of coupling. It has been shown that the inserted exterior perturbation depending on chain parameters can damp, increase, spread without modifications along the chain and evolve to а stable space-time structure, namely, the solitary impulse. This one is not «stationary» for its profile is changed either periodically or chaotically during discrete time.

Key words: 
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Acknowledgments: 
In conclusion, the author expresses gratitude to D.I. Trubetskov for his constant attention and support, as well as to V.I. Ponomarenko for a number of valuable tips used by the author in writing this work.
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Received: 
01.07.1996
Accepted: 
22.10.1996
Published: 
10.12.1996
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