Abstract
The study of the chaotic dynamics in fractional-order maps has received great attention in the past years. This chapter proposes 2D and 3D fractional maps based on the Caputo difference operator. The dynamics of these fractional systems are experimentally investigated via bifurcation diagrams, phase portraits, the maximum Lyapunov exponent, and the 0-1 test. Results show that the 2D fractional map shows coexistence of different types of periodic attractors and chaotic attractors. Additionally, the dynamics and complexity of the 3D fractional map shows high complexity as the fractional order decreases.
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