Coexisting attractors, amplitude control, circuit implementation of grid-scroll memristive hyperchaotic oscillator and its application in underwater signal detection

Abstract

Chaotic oscillators play an indispensable role in chaos-based engineering applications. This study proposes a novel grid-scroll memristive hyperchaotic system with infinite equilibrium points and applies it to weak signal detection. First, a novel controllable grid-scroll memristive hyperchaotic system with multi-dimensional extended attractors is designed based on the smooth flux-controlled non-volatile memristor and the piecewise linear function. The system can generate n × n-scroll hyperchaotic attractors in y and z dimensions, with each independent attractor exhibits a similar topological structure. The linear offset switch induced by the piecewise linear function enables the infinite extension of the attractor. Numerical analysis demonstrates that the system has infinitely coexisting single-scroll and multi-scroll attractors, while a built-in parameter enabling global amplitude control is also validated. The analog circuit of the grid-scroll hyperchaotic system is implemented to validate its practical applicability. Then, based on the 2 × 2-scroll hyperchaotic oscillator, combined with the complete empirical mode decomposition with adaptive noise (CEEMDAN) and Hilbert transform, a new underwater acoustic signal detection model is constructed. Compared with the traditional detection models, the designed model not only exhibits higher sensitivity to periodic signals, stronger immunity to various noises, but also easier to distinguish the state changes of the attractor. The experimental results demonstrate that the minimum detection SNR of the detection model can reach −63 dB, and the accuracy of frequency extraction exceeds 99.9 %. The successful detection of ship radiated noise confirms the engineering feasibility of the proposed model.