Abstract
This paper utilizes the 0–1 test algorithm to identify chaos in a fractional chaotic map. A fractional Burgers map is proposed by means of the Caputo-like delta difference operator. The bifurcation diagrams, phase trajectories and 0–1 test results of the fractional Burgers map are presented, respectively. This work extends the 0–1 test algorithm to the discrete fractional chaotic map.
Highlights
The fractional systems have recently received increasing attention, because fractional calculus can accurately explain many realistic problems
In order to avoid the construction of a Jacobian matrix, in this paper we extend the 0–1 test algorithm [22,23,24,25,26,27,28] to a fractional chaotic map, which provides another reference for the study of the fractional chaotic map
4 The chaotic dynamics of fractional Burgers map The chaos of fractional Burgers map is identified by using the recently proposed 0–1 test
Summary
The fractional systems have recently received increasing attention, because fractional calculus can accurately explain many realistic problems. The studies on discrete fractional systems are still in their infancy, especially in chaos dynamics. Researchers get more interesting results for discrete fractional chaotic systems by means of [15,16,17,18,19,20].
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