Inverse full state hybrid projective synchronization for chaotic maps with different dimensions |
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Authors: | Adel Ouannas Giuseppe Grassi |
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Institution: | 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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Keywords: | chaotic map full state hybrid projective synchronization inverse problem maps with different dimensions |
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