Synchronization of nonlinear fractional order systems

Rafael Martínez-Martínez; Juan L. Mata-Machuca; Rafael Martínez-Guerra; Jorge A. León; Guillermo Fernández-Anaya

doi:10.1016/j.amc.2011.08.075

Synchronization of nonlinear fractional order systems

Rafael Martínez-Martínez, Juan L. Mata-Machuca, Rafael Martínez-Guerra, Jorge A. León, Guillermo Fernández-Anaya

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

This paper deals with the master-slave synchronization scheme for partially known nonlinear fractional order systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown state variables. For solving this problem we introduce a Fractional Algebraic Observability (FAO) property which is used as a main tool in the design of the master system. As numerical examples we consider a fractional order Rössler hyperchaotic system and a fractional order Lorenz chaotic system and by means of some simulations we show the effectiveness of the suggested approach.

Original language	English
Pages (from-to)	3338-3347
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	218
Issue number	7
DOIs	https://doi.org/10.1016/j.amc.2011.08.075
State	Published - 1 Dec 2011
Externally published	Yes

Keywords

Fractional Algebraic Observability
Fractional chaotic systems
Fractional hyperchaotic systems
Nonlinear fractional order systems
Synchronization

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10.1016/j.amc.2011.08.075

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title = "Synchronization of nonlinear fractional order systems",

abstract = "This paper deals with the master-slave synchronization scheme for partially known nonlinear fractional order systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown state variables. For solving this problem we introduce a Fractional Algebraic Observability (FAO) property which is used as a main tool in the design of the master system. As numerical examples we consider a fractional order R{\"o}ssler hyperchaotic system and a fractional order Lorenz chaotic system and by means of some simulations we show the effectiveness of the suggested approach.",

keywords = "Fractional Algebraic Observability, Fractional chaotic systems, Fractional hyperchaotic systems, Nonlinear fractional order systems, Synchronization",

author = "Rafael Mart{\'i}nez-Mart{\'i}nez and Mata-Machuca, {Juan L.} and Rafael Mart{\'i}nez-Guerra and Le{\'o}n, {Jorge A.} and Guillermo Fern{\'a}ndez-Anaya",

note = "Funding Information: R. Mart{\'i}nez-Mart{\'i}nez and J. L. Mata-Machuca gratefully acknowledge to CONACyT (M{\'e}xico) for the corresponding postgraduate scholarships. This work was partially supported by the CONACyT Grant 98998.",

year = "2011",

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doi = "10.1016/j.amc.2011.08.075",

language = "Ingl{\'e}s",

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AU - Martínez-Martínez, Rafael

AU - Mata-Machuca, Juan L.

AU - Martínez-Guerra, Rafael

AU - León, Jorge A.

AU - Fernández-Anaya, Guillermo

N1 - Funding Information: R. Martínez-Martínez and J. L. Mata-Machuca gratefully acknowledge to CONACyT (México) for the corresponding postgraduate scholarships. This work was partially supported by the CONACyT Grant 98998.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - This paper deals with the master-slave synchronization scheme for partially known nonlinear fractional order systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown state variables. For solving this problem we introduce a Fractional Algebraic Observability (FAO) property which is used as a main tool in the design of the master system. As numerical examples we consider a fractional order Rössler hyperchaotic system and a fractional order Lorenz chaotic system and by means of some simulations we show the effectiveness of the suggested approach.

AB - This paper deals with the master-slave synchronization scheme for partially known nonlinear fractional order systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown state variables. For solving this problem we introduce a Fractional Algebraic Observability (FAO) property which is used as a main tool in the design of the master system. As numerical examples we consider a fractional order Rössler hyperchaotic system and a fractional order Lorenz chaotic system and by means of some simulations we show the effectiveness of the suggested approach.

KW - Fractional Algebraic Observability

KW - Fractional chaotic systems

KW - Fractional hyperchaotic systems

KW - Nonlinear fractional order systems

KW - Synchronization

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U2 - 10.1016/j.amc.2011.08.075

DO - 10.1016/j.amc.2011.08.075

M3 - Artículo

SN - 0096-3003

VL - 218

SP - 3338

EP - 3347

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 7

ER -

Synchronization of nonlinear fractional order systems

Abstract

Keywords

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