On fractional order maps and their synchronization

We study the stability of linear fractional order maps. We show that in the stable region, the evolution is described by Mittag-Leffler functions and a well defined effective Lyapunov exponent can be obtained in these cases. For one-dimensional systems, this exponent can be related to the corresponding fractional differential equation. A fractional equivalent of map $f(x)=ax$ is stable for $a_c(\alpha)

Keywords:

• Eigenvalues and eigenvectors
• Mathematical analysis
• Function (mathematics)
• Nonlinear system
• Lyapunov exponent
• Fixed point
• Physics
• Normal mode
• Stability (probability)
• Exponent

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