Discrete Exponential Memristor-Coupled Multistable Hyperchaotic Attractor

Discrete memristive chaotic maps are promising for secure communications due to their digital compatibility, yet existing designs face limitations, including narrow hyperchaotic ranges and a single type of chaotic attractor. This paper proposes a family of 2D hyperchaotic maps by coupling a discrete exponential memristor with four 1D seed maps. Theoretical analysis reveals that the exponential memristor induces non-hyperbolic fixed points and periodicity with respect to the memristor’s initial charge, enabling controlled coexistence of both homogeneous and heterogeneous multistable attractors. Numerical simulations show two positive Lyapunov exponents (LEs) and broad hyperchaotic regions; the memristor-coupled Sine map achieves a maximum LE of 0.4963 and spectral entropy (SE) of 0.8915, outperforming representative cosine- and quadratic-based benchmarks. A pseudorandom number generator (PRNG) passes all National Institute of Standards and Technology (NIST) SP 800-22 tests. STM32F407-based hardware experiments confirm physical realizability, and an image encryption application demonstrates near-ideal entropy (7.9883) and strong differential attack resistance. These results establish the discrete exponential memristor as an effective nonlinearity for enriching chaos complexity and hardware-oriented security primitives.