Generation of multitype, multicavity chaotic attractors via impulse-function-based state variable extension

This paper proposes a universal impulse-function-based method for extending discrete chaotic maps, enabling flexible construction of multicavity chaotic attractors. The proposed method achieves one-directional (1D)/two-directional (2D) extensions without introducing additional nonlinear terms or altering system stability. Theoretically, the cavity quantity in arbitrary directions is controlled by adjusting impulse levels N, while the amplitude regulation is implemented through modifications to the proportionality parameter ρ. Theoretical analyses, including Lyapunov exponents (LEs) and bifurcation diagrams, are conducted, confirming that the extended maps retain the intrinsic dynamics of five rational map classes. The field-programmable gate array (FPGA) implementation results are consistent with the numerical simulation results, verifying the correctness of the theoretical analysis. The method enables the expansion of unipolar attractors and enhances entropy metrics, offering a robust framework for applications in secure communication, encryption, and chaos-based technologies.