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On Inverse Full State Hybrid Function Projective Synchronization For Continuous-time Chaotic Dynamical Systems with Arbitrary Dimensions

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Abstract

Referring to continuous-time chaotic dynamical systems, this paper investigates the inverse full state hybrid function projective synchronization (IFSHFPS) of non-identical systems characterized by different dimensions. By taking a master system of dimension n and a slave system of dimension m, the method enables each master system state to be synchronized with a linear combination of slave system states, where the scaling factor of the linear combination can be any arbitrary differentiable function. The approach, based on the Lyapunov stability theory and stability of linear continuous-time systems, presents some useful features: (i) it enables non-identical chaotic systems with different dimension \(n<m\) or \(n>m\) to be synchronized; (ii) it can be applied to a wide class of chaotic (hyperchaotic) systems for any differentiable scaling function; (iii) it is rigorous, being based on two theorems, one for the case \(n<m\) and the other for the case \(n>m\). Two different numerical examples are reported. The examples clearly highlight the capability of the conceived approach in effectively achieving synchronized dynamics for any differentiable scaling function.

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Authors and Affiliations

  1. Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, Tebessa, 12002, Algeria

    Adel Ouannas

  2. Faculty of computers and information, Benha University, Banha, Egypt

    Ahmad Taher Azar

  3. Nile University, Giza, Egypt

    Ahmad Taher Azar

  4. Department of Material Sciences, University of Tebessa, 12002, Tebessa, Algeria

    Toufik Ziar

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  1. Adel Ouannas
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  2. Ahmad Taher Azar
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  3. Toufik Ziar
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Correspondence to Ahmad Taher Azar.

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Ouannas, A., Azar, A.T. & Ziar, T. On Inverse Full State Hybrid Function Projective Synchronization For Continuous-time Chaotic Dynamical Systems with Arbitrary Dimensions. Differ Equ Dyn Syst 28, 1045–1058 (2020). https://doi.org/10.1007/s12591-017-0362-x

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