Design And Application Of Adjustable Amplitude Discrete Hyperchaotic Mappin

With the wide application of chaos and the in-depth study of chaotic dynamic systems,the controllability of chaotic oscillation and chaotic mapping has gradually become a research hotspot.The single-parameter control of continuous chaotic systems has been widely studied.However,the single-parameter control of discrete chaotic maps has not received much attention.The purpose of this paper is to construct discrete chaotic maps with single-parameter amplitude control,revealing potential amplitude control parameters in different nonlinear discrete maps,and circuit experiments verify the amplitude control properties of chaotic maps.The main work of this paper includes:The amplitude controllable two-dimensional hyperchaotic map is constructed.The fixed point and its stability,bifurcation behavior and bistable characteristics of the discrete map are analyzed,and two independent amplitude control parameters are found,realizing the local and global amplitude modulation of the hyperchaotic output.The verification of hyperchaotic mapping is realized based on STM32 microcontroller circuit.A three-dimensional hyperchaotic map with controllable amplitude and homogeneous multistability is constructed.By discretizing a continuous chaotic system and introducing a sine function to construct a discrete chaotic map,two independent single-parameter amplitude controls are realized.It is found that the initial value of the mapping can also realize the amplitude control of the discrete sequence,thus presenting the phenomenon of homogeneous multi-stable state.The application of amplitude controllable hyperchaotic map in image encryption is studied.Based on the DNA coding principle and coding process,a new image encryption algorithm is constructed.The application effect of image encryption based on adjustable amplitude discrete chaotic map is studied,and the image encryption performance under this algorithm is comprehensively analyzed.