A Hyperchaotic Neural Network with Multi-Structure Attractors and Its Application in PRNG

Abstract

Memristive Hopfield neural networks (HNNs) have been widely explored for chaotic signal generation and data encryption owing to their rich dynamical behaviors. However, most existing memristive HNN models suffer from limited controllability of the number of coexisting attractors, insufficient dimensional complexity of chaotic dynamics, and weak adaptability to industrial grayscale image encryption scenarios. To address these issues, this paper proposes a novel memristive HNN model with a single magnetic flux-coupling memristor and systematically investigates its dynamical characteristics and pseudo-random number generator application. The scope of this work covers mathematical modeling, quantitative dynamical analysis, and pseudo-random number generator (PRNG) construction and verification. Theoretical derivation and numerical simulations demonstrate that the proposed system exhibits hyperchaotic behavior with two positive Lyapunov exponents and achieves flexible tuning of coexisting attractor numbers via piecewise parameters M and N, following the relation N + M + 2. The Kaplan–Yorke dimension of the system is calculated as 3.558, verifying its high-dimensional chaotic complexity. Based on the hyperchaotic sequences generated by the model, a PRNG is constructed and passes all test items of the NIST SP 800-22 test suite over 1000 non-overlapping 1 Mbit streams, providing a reliable chaotic sequence source for industrial data security scenarios. This work provides a feasible dynamical model for industrial data security scenarios and offers a reference for the controllable design of multi-stable memristive neural networks.