Extremely multi-stable grid-scroll memristive chaotic system with omni-directional extended attractors and application of weak signal detection

The extreme multi-stability and omni-directional expansion of the attractors in chaotic systems play an indispensable role in the chaos-based engineering applications. In this study, a novel extremely multi-stable grid-scroll memristive chaotic system with omni-directional extended attractors is proposed, and applies it to weak signal detection. Firstly, a flux-controlled non-volatile memristor with a typical 8-shaped pinched hysteresis loop, and three piecewise linear functions that can promote the position offset of the attractor are designed. On this basis, we construct a novel grid-scroll memristive chaotic system with infinite equilibrium points, which can generate n × n × n-scroll attractors. The piecewise linear functions lead to the infinite expansion of the chaotic attractor in the x, y, and z directions, which also indirectly causes the position offset in the w direction. This phenomenon has not been discovered in existing researches. The numerical analysis demonstrates that the memristive chaotic system has infinite coexisting attractors, and a built-in parameter that can achieve global amplitude control of the attractor has also been verified. The omni-directional expansion, coexistence and global amplitude control of the attractor illustrates the extreme multi-stability of the designed system. The analog circuit of the memristive chaotic system has been implemented to verify its feasibility and practicability. Finally, a weak signal detection system based on the grid-scroll memristive chaotic system is constructed. This system not only has excellent robustness to various noise, but also is more sensitive to weak periodic signals. The detection signal-to-noise ratio (SNR) threshold reaches -63 dB. The applicability of this method in practical engineering is verified through the detection of ship radiation signals submerged in ocean background noise.