https://doi.org/10.1140/epjp/s13360-025-06542-3
Regular Article
Analysis of 3D chaotic system with novel double scroll structure and additional nonlinear functions and its application in weak signal detection
School of Electronic Engineering, Xi’an University of Posts and Telecommunications, 710121, Xi’an, Shaanxi, China
Received:
21
April
2025
Accepted:
7
June
2025
Published online:
7
July
2025
To overcome the limitations of the traditional two-dimensional chaotic system in detection performance, a three-dimensional (3D) chaotic system with novel double scroll structure and additional nonlinear functions is proposed in this paper, and it is applied to the detection of underwater acoustic signals. Firstly, the dynamic characteristics of the double scroll chaotic system are systematically studied through nonlinear dynamic analysis methods such as bifurcation diagram, power spectrum analysis and Poincaré section. It is found that the system exhibits unique coexistence attractor phenomenon and significant offset boosting effect, and the feasibility of the system is verified by the implementation of Simulink and Multisim. On this basis, a weak signal detection system based on double scroll chaotic system is constructed, and the phase transition threshold of the system is determined by double verification method. After performance testing, the detection signal-to-noise ratio lower limit can reach 
dB. Then, based on the proposed chaotic system, an underwater acoustic weak signal detection method based on double scroll chaotic system is proposed. In terms of weak signal amplitude detection, the method based on phase trajectory analysis is used to achieve accurate detection of square wave signals under colored noise background. In terms of weak signal frequency detection, the frequency band range of the signal to be measured is determined by scaling transformation and oscillator array frequency scanning method, and combined with Hilbert transform, high-precision detection of unknown signal frequency is achieved. Finally, the detection method is verified by using simulated signals and measured ship signals. The results show that the relative error of this method is always kept within 0.98%, showing excellent performance in the detection of underwater acoustic weak signal in complex marine environments. This research result provides new technical means for underwater target detection and marine environment monitoring.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
