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A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems

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  • Aguirre-Hernández, B.
  • Campos-Cantón, E.
  • López-Renteria, J.A.
  • Díaz González, E.C.

Abstract

In this paper, we consider characteristic polynomials of n-dimensional systems that determine a segment of polynomials. One parameter is used to characterize this segment of polynomials in order to determine the maximal interval of dissipativity and unstability. Then we apply this result to the generation of a family of attractors based on a class of unstable dissipative systems (UDS) of type affine linear systems. This class of systems is comprised of switched linear systems yielding strange attractors. A family of these chaotic switched systems is determined by the maximal interval of perturbation of the matrix that governs the dynamics for still having scroll attractors.

Suggested Citation

  • Aguirre-Hernández, B. & Campos-Cantón, E. & López-Renteria, J.A. & Díaz González, E.C., 2015. "A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 100-106.
    • Handle: RePEc:eee:chsofr:v:71:y:2015:i:c:p:100-106
    DOI: 10.1016/j.chaos.2014.12.012
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    References listed on IDEAS

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    1. Kuetche Mbe, E.S. & Fotsin, H.B. & Kengne, J. & Woafo, P., 2014. "Parameters estimation based adaptive Generalized Projective Synchronization (GPS) of chaotic Chua’s circuit with application to chaos communication by parametric modulation," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 27-37.
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    4. Ahmad, Wajdi M., 2005. "Generation and control of multi-scroll chaotic attractors in fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 727-735.
    5. Krawiecki, A., 2014. "Chaotic synchronization on complex hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 44-50.
    6. Bouallegue, Kais & Chaari, Abdessattar & Toumi, Ahmed, 2011. "Multi-scroll and multi-wing chaotic attractor generated with Julia process fractal," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 79-85.
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    Cited by:

    1. Pai, Ming-Chang, 2015. "Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 757-767.
    2. Zhong, Xiaoyun & Peng, Minfang & Tse, Chi K. & Guo, Shangjiang & Shahidehpour, Mohammad, 2015. "Analysis and control of multiple chaotic attractors from a three-dimensional system," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 138-150.

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