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Chaos in discrete fractional difference equations

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Abstract

Recently, the discrete fractional calculus (DFC) is receiving attention due to its potential applications in the mathematical modelling of real-world phenomena with memory effects. In the present paper, the chaotic behaviour of fractional difference equations for the tent map, Gauss map and 2x(mod 1) map are studied numerically. We analyse the chaotic behaviour of these fractional difference equations and compare them with their integer counterparts. It is observed that fractional difference equations for the Gauss and tent maps are more stable compared to their integer-order version.

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Authors and Affiliations

  1. Department of Mathematics, Savitribai Phule Pune University, Pune, 411 007, India

    AMEY DESHPANDE & VARSHA DAFTARDAR-GEJJI

  2. Department of Mathematics, College of Engineering Pune, Pune, 411 005, India

    AMEY DESHPANDE

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  1. AMEY DESHPANDE
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  2. VARSHA DAFTARDAR-GEJJI
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Correspondence to VARSHA DAFTARDAR-GEJJI.

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DESHPANDE, A., DAFTARDAR-GEJJI, V. Chaos in discrete fractional difference equations. Pramana - J Phys 87, 49 (2016). https://doi.org/10.1007/s12043-016-1231-9

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  • DOI: https://doi.org/10.1007/s12043-016-1231-9

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