Initial-condition-based multi-attractor generation in 3d grid-scroll chaotic structure: the IG-MAG approach

Abstract

This study introduces the initial-grid multi-attractor generation (IG-MAG) approach for generating multi-attractor structures in three-dimensional grid-scroll chaotic systems. The method systematically shifts the initial conditions, implemented as initial-offset control, across a predefined folding-based grid-scroll structure without modifying the system parameters. Numerical results indicate that, without modifying the system parameters or introducing memristive extensions, 27 spatially separated chaotic grid cells can be obtained under the configuration Mx=My=Mz=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_x = M_y = M_z =$$\end{document} 1. The chaotic behavior within representative grid cells is characterized through the Lyapunov exponent spectrum and the Kaplan-Yorke fractal dimension analysis, where consistent mean and variance characteristics are observed across different grid locations. To demonstrate numerical scalability, extended grid configurations up to Mx=My=Mz=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_x = M_y = M_z =$$\end{document} 5, corresponding to 1331 grid cells, are also examined, and the persistence of chaotic behavior is confirmed for selected grid cells. In addition, the applicability of the IG-MAG framework is numerically illustrated on the Lorenz system, indicating that the proposed initial-grid-based strategy can be transferred to other continuous-time chaotic models through appropriate grid spacing selection. Overall, the results indicate that the IG-MAG approach provides a numerically extendable multistability framework under fixed system parameters and may serve as a structured basis for future chaos-based security-oriented applications such as multi-user chaotic stream allocation and key-related studies.