Initial-offset and amplitude control of multi-scroll attractor in a chaotic jerk system

Abstract With the gradual deepening of research on chaos, in order to flexibly apply chaos, offset boosting and amplitude control have become a hot topic. However, few people have studied chaotic systems with multi-scroll attractor under initial conditions. This paper constructs and analyzes a simple four-dimensional chaotic system. Unlike other extension methods that modify the original seed system, this method does not make any changes to the original seed system, only adds a new variable in the extension dimension. It is found that the proposed system can achieve offset boosting and amplitude control by changing the initial values, and the system has characteristics such as multi-scroll attractors, infinite equilibrium points, symmetry, and so on. Finally, FPGA hardware implementation was carried out to verify the numerical results.