Designing n-D Non-Degenerate Hyperchaotic Systems via a Simple Circulant Matrix

To counteract the dynamic deterioration of digitized chaotic systems, we propose a mathematical model for generating <tex-math notation="LaTeX">n </tex-math> -D non-degenerate hyperchaotic systems (NHS) with <tex-math notation="LaTeX">n </tex-math> positive Lyapunov exponents (LEs) and complex dynamic behaviors. In this brief, we analyze the internal relations among the coefficients, eigenvalues, and singular values of a circulant matrix. Based on singular value decomposition, the <tex-math notation="LaTeX">n </tex-math> -D NHS can be constructed by presetting a conjugate symmetric vector, with a theoretical proof provided. The LEs of the <tex-math notation="LaTeX">n </tex-math> -D NHS can be adjusted arbitrarily by changing a preconfigured eigenvalue vector. We demonstrate the feasibility and efficacy of the proposed scheme with two examples, a 4-D NHS and a 5-D NHS. Based on the 5-D NHS, we design a simple pseudorandom number generator (PRNG) with desirable statistical properties. The proposed NHS model has fewer control coefficients, making it suitable for applications in IoT security and lightweight chaotic cryptography.