Abstract
In this paper, the dynamical behaviors of fractional q-deformation chaotic map are analyzed. Firstly, the fractional q-deformation chaotic map is proposed by employing the Caputo delta difference operator. Secondly, the rich dynamical behaviors, such as numerically stable period (NSP) attractor, quasi-periodic attractor, strange nonchaotic attractor, and chaotic attractor, of the proposed map are discussed by utilizing bifurcation diagram, phase diagram, and 0–1 test. Thirdly, two controllers are designed to study the chaos control and synchronization of the fractional q-deformation chaotic map. Finally, numerical simulations are presented to demonstrate the findings.
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