Abstract
Some endeavors have been recently dedicated to explore the dynamic properties of the fractional-order discrete-time chaotic systems. To date, attention has been mainly focused on fractional-order discrete-time systems with “self-excited attractors.” This paper makes a contribution to the topic of fractional-order discrete-time systems with “hidden attractors” by presenting a new 2-dimensional discrete-time system without equilibrium points. The conceived system possesses an interesting property not explored in the literature so far, i.e., it is characterized, for various fractional-order values, by the coexistence of various kinds of chaotic attractors. Bifurcation diagrams, computation of the largest Lyapunov exponents, phase plots, and the 0-1 test method are reported, with the aim to analyze the dynamics of the system, as well as to highlight the coexistence of chaotic attractors. Finally, an entropy algorithm is used to measure the complexity of the proposed system.
Highlights
Exploring chaotic dynamics has received considerable attention during the past few years [1]
This paper aims to make a contribution to the topic of fractional-order discrete-time systems (FoDs) with “hidden attractors” by presenting a new 2Dimensional FoDs (2D-FoDs) without equilibrium points. e conceived system possesses an interesting property, i.e., it is characterized by the coexistence of various kinds of chaotic attractors
An entropy algorithm is used to measure the complexity of the proposed system
Summary
Exploring chaotic dynamics has received considerable attention during the past few years [1]. The presence of chaos in the fractionalorder discrete double scroll map has been investigated in [14], whereas in [12], the fractional-order delayed logistic map was analyzed regarding to its chaotic behavior. In [15], the dynamics of the fractional-order version of the standard iterated map have been investigated, whereas in [18], a 2Dimensional FoDs (2D-FoDs) without discontinuity for all equations of the system has been presented. These FoMs with “hidden attractors” do not show any coexisting chaotic attractors. A number of phase plots are reported, which highlight the coexistence of several types of chaotic attractors for various fractional-order values of the conceived system
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