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Complex dynamics and multiple coexisting attractors in a fractional-order microscopic chemical system

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Abstract

In this paper, we proposed a fractional-order microscopic chaotic system, derived from a set of microscopic chemical reactions. The dynamical properties of the proposed model have been investigated through Lyapunov characteristic exponents, bifurcation, spectral entropy and C0 complexity algorithm. The results show that the system has rich dynamics in derivative order and the system parameter. In addition, multiple coexisting attractors are found in the system by selecting appropriate initial values. Complexity measuring algorithms are developed as an effective tool for the detection of such attractors. The results are effective for the dynamical randomness in the collisional motion of atoms and molecules in fluids to produce the deterministic chemical chaos, even in fractional order.

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Authors and Affiliations

  1. School of Physics and Electronics, Central South University, Changsha, 410083, P.R. China

    Shaobo He & Kehui Sun

  2. Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia

    Santo Banerjee

  3. Malaysia-Italy Centre of Excellence for Mathematical Science, Universiti Putra Malaysia, Serdang, Malaysia

    Santo Banerjee

Authors
  1. Shaobo He
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  2. Santo Banerjee
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  3. Kehui Sun
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Corresponding author

Correspondence to Santo Banerjee.

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He, S., Banerjee, S. & Sun, K. Complex dynamics and multiple coexisting attractors in a fractional-order microscopic chemical system. Eur. Phys. J. Spec. Top. 228, 195–207 (2019). https://doi.org/10.1140/epjst/e2019-800166-y

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  • DOI: https://doi.org/10.1140/epjst/e2019-800166-y

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