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Chin. Phys. B, 2016, Vol. 25(9): 090503    DOI: 10.1088/1674-1056/25/9/090503
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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
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).
Keywords:  chaotic map      full state hybrid projective synchronization      inverse problem      maps with different dimensions  
Received:  22 November 2015      Revised:  06 March 2016      Published:  05 September 2016
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Xt (Synchronization; coupled oscillators)  
Corresponding Authors:  Adel Ouannas, Giuseppe Grassi     E-mail:  ouannas_adel@yahoo.fr;giuseppe.grassi@unisalento.it

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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