Abstract
In this paper, a novel three dimensional fractional-order map is proposed. This fractional map has no fixed point, but it can also exhibit rich and complex dynamical behavior. The dynamical properties of the new model are investigated by applying numerical tools such as bifurcation diagram, maximum Lyapunov exponent, phase portraits, and evolution of states. It shows that the fractional order map is more complex when the fractional order is small.
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