Design and DSP implementation of structurally non-uniform multi-scroll attractors based on novel modified sawtooth functions

Conventional multi-scroll chaotic systems (MSCSs) typically exhibit uniform scroll distributions, limiting the diversity of attractor structures. In contrast, non-uniformly distributed MSCSs can overcome this constraint, which enables more flexible attractor configurations and enhances their potential in practical engineering applications. In this study, five modified sawtooth wave functions are proposed and embedded into a three-dimensional chaotic system to generate five types of multi-scroll attractors with irregular spatial distributions, including (1) attractors with enlarged scroll structures on both sides, (2) attractors with an enlarged central scroll structure, (3) attractors with a central separation structure, (4) attractors with enlarged scroll structures at the center and both sides, and (5) attractors with separated scrolls and enlarged side scrolls. Among these, the third and fifth types exhibit attractor coexistence. Furthermore, by selecting and combining two different modified sawtooth functions, four types of grid multi-scroll attractors are constructed: (1) attractors with separated structures and varying scroll sizes, (2) attractors with cross-shaped separated structures, (3) attractors with a double-chain structure, and (4) attractors with a triple-chain structure. Among them, the cross-shaped type also exhibits attractor coexistence. This study systematically analyses the generation mechanisms of these non-uniform multi-scroll attractors and examines their offset-boosting phenomenon. The chaotic characteristics of different types of attractors are analyzed using the largest Lyapunov exponent, bifurcation diagrams, and spectral entropy. In addition, the National Institute of Standards and Technology test is employed to validate the randomness of the proposed systems. Finally, hardware implementation on a digital signal processing platform confirms its applicability for practical engineering applications.