Adaptative synchronization in multi-output fractional-order complex dynamical networks and secure communications

  • Juan L. Mata-MachucaEmail author
  • Ricardo Aguilar-López
Regular Article
Part of the following topical collections:
  1. Focus Point on Systems and Security: Advanced Methods with Chaos and Complexity


This work deals with the adaptative synchronization of complex dynamical networks with fractional-order nodes and its application in secure communications employing chaotic parameter modulation. The complex network is composed of multiple fractional-order systems with mismatch parameters and the coupling functions are given to realize the network synchronization. We introduce a fractional algebraic synchronizability condition (FASC) and a fractional algebraic identifiability condition (FAIC) which are used to know if the synchronization and parameters estimation problems can be solved. To overcome these problems, an adaptative synchronization methodology is designed; the strategy consists in proposing multiple receiver systems which tend to follow asymptotically the uncertain transmitters systems. The coupling functions and parameters of the receiver systems are adjusted continually according to a convenient sigmoid-like adaptative controller (SLAC), until the measurable output errors converge to zero, hence, synchronization between transmitter and receivers is achieved and message signals are recovered. Indeed, the stability analysis of the synchronization error is based on the fractional Lyapunov direct method. Finally, numerical results corroborate the satisfactory performance of the proposed scheme by means of the synchronization of a complex network consisting of several fractional-order unified chaotic systems.


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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Instituto Politécnico Nacional, Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías AvanzadasAcademia de MecatrónicaCiudad de MéxicoMexico
  2. 2.CINVESTAV-IPNDepartamento de Biotecnología y BioingenieríaCiudad de MéxicoMexico

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