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Deterministic coherence resonance analysis of coupled chaotic oscillators: fractional approach

Author

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  • Gilardi-Velázquez, H.E.
  • Echenausía-Monroy, J.L.
  • Jaimes-Reátegui, R.
  • García-López, J.H.
  • Campos, Eric
  • Huerta-Cuellar, G.

Abstract

Recently, the stabilization of chaos by chaos has attracted the attention of researchers. A small deviation between the natural frequencies of unidirectionally coupled chaotic oscillators can cause the emerge of a coherence resonance in the slave oscillator for a given coupling strength. In this work, we investigate the phenomenon of coherence resonance for a coupled Rössler system under the influence of fractional operators in the frequency response of the slave oscillator. Based on the analysis of the fractional Rössler system, we determine a range of fractional orders in which the system retains its instability, and an analysis of the frequency response of the system to changes in natural frequency is developed. Finally, the frequency response of the slave system to changes in the fractional derivative order, the natural frequency of the master system, and the coupling strength is analyzed, and how these changes promote the occurrence of coherence resonance is examined.

Suggested Citation

  • Gilardi-Velázquez, H.E. & Echenausía-Monroy, J.L. & Jaimes-Reátegui, R. & García-López, J.H. & Campos, Eric & Huerta-Cuellar, G., 2022. "Deterministic coherence resonance analysis of coupled chaotic oscillators: fractional approach," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001291
    DOI: 10.1016/j.chaos.2022.111919
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    References listed on IDEAS

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    1. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    2. Zhang, Weiwei & Zhou, Shangbo & Li, Hua & Zhu, Hao, 2009. "Chaos in a fractional-order Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1684-1691.
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    1. Echenausía-Monroy, J.L. & Gilardi-Velázquez, H.E. & Wang, Ning & Jaimes-Reátegui, R. & García-López, J.H. & Huerta-Cuellar, G., 2022. "Multistability route in a PWL multi-scroll system through fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Emanuel Guariglia & Rodrigo C. Guido & Gabriel J. P. Dalalana, 2023. "From Wavelet Analysis to Fractional Calculus: A Review," Mathematics, MDPI, vol. 11(7), pages 1-12, March.

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