Construction Algorithm of N -Dimensional Nondegenerate Polynomial Chaotic Systems

Higher-dimensional nondegenerate chaotic maps can provide complex dynamical behavior for digital-chaos sequence generation, but existing construction methods face a trade-off among Lyapunov-spectrum regulation, computational cost, and state-variable coupling. Decomposition-based methods may require singular value decomposition, QR decomposition, or matrix inversion, whereas conventional triangular constructions may weaken nonlinear interaction because of their sparse structures. To balance these factors, this paper proposes an [Formula: see text]-dimensional nondegenerate polynomial chaotic-system construction based on iterative block-triangular matrix expansion. The method embeds [Formula: see text] diagonal blocks with complex-conjugate eigenvalues and introduces nonlinear polynomial couplings through selected off-diagonal blocks. Under the constant opposite-sign off-diagonal assumption, the diagonal-block structure provides a basis for constructing positive Lyapunov exponents in both even- and odd-dimensional cases. The proposed method avoids matrix decomposition and inversion and has dominant arithmetic and packed-storage growth of [Formula: see text]. Four-dimensional and five-dimensional examples are demonstrated. The numerical results show positive Lyapunov exponent spectra, pronounced trajectory sensitivity, entropy values close to their reference levels, satisfactory statistical randomness of the output-mixed binary sequences, and favorable finite-precision period behavior under the tested settings. These results support the effectiveness of the proposed dimension-general construction and characterize its dynamical and digital behavior.