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Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions |
Adel Ouannas1, Giuseppe Grassi2 |
1. Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, Tebessa 12002, Algeria; 2 Università del Salento, Dipartimento Ingegneria Innovazione, 73100 Lecce, Italy |
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Abstract A new synchronization scheme for chaotic (hyperchaotic) maps with different dimensions is presented. Specifically, given a drive system map with dimension n and a response system with dimension m, the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states. The method, based on the Lyapunov stability theory and the pole placement technique, presents some useful features: (i) it enables synchronization to be achieved for both cases of n < m and n > m; (ii) it is rigorous, being based on theorems; (iii) it can be readily applied to any chaotic (hyperchaotic) maps defined to date. Finally, the capability of the approach is illustrated by synchronization examples between the two-dimensional Hénon map (as the drive system) and the three-dimensional hyperchaotic Wang map (as the response system), and the three-dimensional Hénon-like map (as the drive system) and the two-dimensional Lorenz discrete-time system (as the response system).
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Received: 22 November 2015
Revised: 06 March 2016
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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05.45.Xt
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(Synchronization; coupled oscillators)
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Corresponding Authors:
Adel Ouannas, Giuseppe Grassi
E-mail: ouannas_adel@yahoo.fr;giuseppe.grassi@unisalento.it
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Cite this article:
Adel Ouannas, Giuseppe Grassi Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions 2016 Chin. Phys. B 25 090503
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