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Synchronization of PWL function-based 2D and 3D multi-scroll chaotic systems

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Abstract

We study the synchronization of a piecewise linear function-based chaotic system. That system generates multiple scrolls in multiple directions (two- and three-directions) on phase space. In this scenario, the design of a controller based on Generalized Hamiltonian forms is possible. As function of control signals, we propose a master–slave synchronization scheme using 2n−1 combinations to drive a nonlinear state observer. Associated with this, the piecewise linear functions of the slave are directly controlled by the state-variables of the master system. We computed the synchronization error for each combinations. Besides, the circuit synthesis based on operational amplifiers validates our synchronization scheme by means of SPICE simulations. We observed that the synchronization error at circuit level depends on the number of the control signals used. Our numerical and SPICE simulation results are in agreement showing the usefulness of the proposed approach.

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Acknowledgements

The first author thanks National Council for Science and Technology (CONACyT/MÉXICO) for the support granted through project “Retención” number 174330.

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Authors and Affiliations

  1. Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Apdo. Postal 542, C.P. 72570, Puebla, Pue., Mexico

    Jesus M. Muñoz-Pacheco, Ernesto Zambrano-Serrano, Olga Félix-Beltrán, Luz C. Gómez-Pavón & Arnulfo Luis-Ramos

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  1. Jesus M. Muñoz-Pacheco
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  2. Ernesto Zambrano-Serrano
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  3. Olga Félix-Beltrán
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  4. Luz C. Gómez-Pavón
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  5. Arnulfo Luis-Ramos
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Correspondence to Jesus M. Muñoz-Pacheco.

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Muñoz-Pacheco, J.M., Zambrano-Serrano, E., Félix-Beltrán, O. et al. Synchronization of PWL function-based 2D and 3D multi-scroll chaotic systems. Nonlinear Dyn 70, 1633–1643 (2012). https://doi.org/10.1007/s11071-012-0562-4

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