Chaos in discrete fractional difference equations

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• 作者：AMEY DESHPANDE ; VARSHA DAFTARDAR-GEJJI
• 关键词：Fractional difference equation ; chaos ; Lyapunov exponent ; Gauss map ; tent map ; discrete fractional calculus.
• 刊名：Pramana
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：87
• 期：4
• 全文大小：1,126 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Astronomy
  Astrophysics
  
• 出版者：Springer India
• ISSN：0973-7111
• 卷排序：87

文摘

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.