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High-dimensional chaotification via differential bivariate regression interpolation: Alternative Lyapunov exponents and conic coordinates characterization

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  • Zhou, Jun

Abstract

By low-dimensional base models stacking and differential bivariate regression (SDBR) interpolating, the paper presents a novel approach for high-dimensional chaos modeling and model extension; alternative Lyapunov exponents and chaos characterization by multi-axis conic coordinates are introduced and examined. Specifically, SDBR interpolating chaotification inherits divergence, gradient and Jacobian matrices of the base models in linear combination form such that stability/instability, alternative Lyapunov exponents of the high-dimensional chaotic models can be specified through the base ones and interpolation weighting. To visualize high-dimensional chaos, conic coordinates and coaxial-projection by multiple axes aligning on the conic surface are created, which accommodate the real axis, rectangular and orthogonal Cartesian coordinates as special cases, and provide multiphasic and polygonal vector characterizations for SDBR interpolating and multi-tiered data encryption. Numerical simulations show high efficiency for chaotification, and reveal new features in terms of alternative Lyapunov exponents.

Suggested Citation

  • Zhou, Jun, 2026. "High-dimensional chaotification via differential bivariate regression interpolation: Alternative Lyapunov exponents and conic coordinates characterization," Chaos, Solitons & Fractals, Elsevier, vol. 209(P1).
    • Handle: RePEc:eee:chsofr:v:209:y:2026:i:p1:s0960077926005643
    DOI: 10.1016/j.chaos.2026.118423
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