Multi-scroll expansion of 3D and 4D Jerk systems and its DSP implement

Abstract

The multi-scroll chaotic systems have significant potential in practical applications. By introducing control functions and modifying variable dimensionality, we achieve both single-scroll and dual-scroll expansions in the three-dimensional Jerk system, with Lyapunov exponent analysis confirming that the system retains its chaotic nature. The distribution of equilibrium points and the bifurcation diagrams further illustrate the scroll generation mechanism. By extending the system to four dimensions, we validate the feasibility of multi-scroll expansion in this higher-dimensional framework through numerical simulations. Furthermore, the DSP implementation demonstrates that the constructed multi-scroll system offers flexibility in both the number and arrangement of scrolls, thus laying a foundation for further research and practical engineering applications.