Abstract
Trigonometric functions were used to construct a 2-D symmetrical hyperchaotic map with infinitely many attractors. The regime of multistability depends on the periodicity of the trigonometric function, which is closely related to the initial condition. For this trigonometric nonlinearity and the introduction of an offset controller, the initial condition triggers a specific multistability evolvement, in which infinitely countless symmetric and asymmetric attractors are produced. Initial condition-triggered offset boosting is explored, combined with constant controlled offset regulation. Furthermore, this symmetric map gives the sequences in various types of asymmetric attractors, in which the polarity balance is maintained by the initial condition and a negative coefficient due to the trigonometric function. Finally, as determined through the hardware implementation of STM32, the corresponding results agree with the numerical simulation.
Highlights
We propose a new type of 2-D symmetric hyperchaotic map, revealing its special phenomenon of symmetrical coexistence
A 2-D hyperchaotic map with a symmetrical structure was constructed by applying trigonometric functions, which exhibited various regimes of multistability
According to the polarity balance induced by the parameters, it can trigger various symmetry evolutions
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. An attractor can obtain full control, including the offset in any dimension [17], under certain conditions coexisting attractors appear in the regime of homogeneous multistablity [18]. In this case, the complex chaotic sequence flexibly switches between unipolar or bipolar, which makes it more applicable in image encryption [19–24]. We propose a new type of 2-D symmetric hyperchaotic map, revealing its special phenomenon of symmetrical coexistence.
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