Abstract
In this paper, we propose two new two-dimensional chaotic maps with closed curve fixed points. The chaotic behavior of the two maps is analyzed by the 0–1 test, and explored numerically using Lyapunov exponents and bifurcation diagrams. It has been found that chaos exists in both fractional maps. In addition, result shows that the proposed fractional maps shows the property of coexisting attractors.
Highlights
In the nineteenth century, fractional calculus had its origin in the generalization of integer order differentiation and integration to non-integer order ones [1,2,3,4,5]
The aim of this paper is to study two new chaotic maps with specific types of fixed points by the application of a new test approach (0–1 test) in order to find out whether or not these systems are chaotic
We investigated the chaotic behavior of new two-dimensional fractional chaotic maps with closed curve fixed points
Summary
Fractional calculus had its origin in the generalization of integer order differentiation and integration to non-integer order (fractional order) ones [1,2,3,4,5]. The fact that research in discrete fractional chaotic systems is still in development [26,27,28,29,30,31,32,33,34], and very few difference equations have been considered, was the motivation of our work. The dynamic behaviors of the considered chaotic systems are investigated numerically using bifurcation diagrams and Lyapunov exponents. These systems possess an interesting property: symmetry.
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