Two-time synchronism and induced synchronization in a Kerr coupler

P. Szlachetka; M. Misiak; K. Grygiel

doi:10.1140/epjd/e2003-00095-7

EPJ

Two-time synchronism and induced synchronization in a Kerr coupler

P. Szlachetka^a, M. Misiak^b and K. Grygiel^c

Nonlinear Optics Division (URL: ) , Institute of Physics, A. Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland

Corresponding authors: ^a This email address is being protected from spambots. You need JavaScript enabled to view it. - ^b This email address is being protected from spambots. You need JavaScript enabled to view it. - ^c This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 9 August 2002
Revised: 20 February 2003
Published online: 29 April 2003

Abstract

A pair $Mathematical equation: $({\bf A},{\bf B})$$ of interacting Kerr oscillators treated as a master coupler sending chaotic or hyperchaotic signals to its slave copy $Mathematical equation: $({\bf a},{\bf b})$$ is considered. We synchronize $Mathematical equation: ${\bf a} $$ with $Mathematical equation: ${\bf A}$$ and $Mathematical equation: ${\bf b}$$ with $Mathematical equation: ${\bf B}$$ through two communication channels $Mathematical equation: ${\bf A} \Rightarrow {\bf a}$$ and $Mathematical equation: ${\bf B}\Rightarrow {\bf b}$$ . The effect of synchronization is non-simultaneous, the pairs $Mathematical equation: $({\bf a}{\bf ,A})$$ and $Mathematical equation: $({\bf b},{\bf B})$$ have different times of synchronization. It is possible to synchronize an individual pair, for example, $Mathematical equation: $({\bf b},{\bf B})$$ when its communication channel $Mathematical equation: ${\bf B} \Rightarrow {\bf b}$$ is turned off, provided that the second channel for the pair $Mathematical equation: $({\bf a},{\bf A})$$ is turned on. The resulted synchronization is termed induced. The efficiencies of the presented synchronization precesses are studied.

PACS: 05.45.Xt – Synchronizations; coupled oscillators / 05.45.Pq – Numerical simulations of chaotic systems / 42.65.Sf – Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics

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EPJ

Two-time synchronism and induced synchronization in a Kerr coupler

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