Synchronization of chaotic systems involving fractional operators of Liouville–Caputo type with variable-order

A. Coronel-Escamilla, J.F. Gómez-Aguilar, L. Torres, R.F. Escobar-Jiménez and M. Valtierra-Rodríguez

Physica A: Statistical Mechanics and its Applications, 2017, vol. 487, issue C, 1-21

Abstract: In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master–slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville–Caputo and Atangana–Baleanu–Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua’s systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0,1] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.

Keywords: Fractional observers; Fractional multi-scrolls attractors; Liouville–Caputo derivative of variable-order; Atangana–Baleanu–Caputo derivative of variable-order; Adams method (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:487:y:2017:i:c:p:1-21

DOI: 10.1016/j.physa.2017.06.008

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