Abstract
In order to improve the complexity of the chaotic system and the accuracy of the weak signal detection, this paper propose a new hidden attractor coupled chaotic system and a corresponding weak signal detection system, which can be used to obtain the phase diagram of the proposed system using the fourth order of the Runge-Kutta method. The dynamic behavior of the chaotic system is analyzed through the bifurcation diagram, Lyapunov exponent, and power spectrum. The Lyapunov exponent is used to depict the basins of attraction for the system. After research, it is discovered that symmetry exists in the system. Comparative analysis has demonstrated that the system has higher detection accuracy and excellent antinoise performance. Finally, the circuit simulation and FPGA realization of the system indicated that the numerical simulation results are consistent with the FPGA implementation results, proving the theoretical analysis to be correct and the accuracy of the detection results.
Highlights
After Lorenz introduced the Lorenz system [1] in 1963, the chaos theory has become a hot spot of nonlinear field research
In [5], the mixed basins of attraction formed when multiple attractors coexist in a chaotic system are analyzed, and the research shows that the basins of attraction have a fractal regular structure
Reference [13] analyzed the multistability of a chaotic system with two circles of equilibrium points and implemented the system using FPGA technology
Summary
After Lorenz introduced the Lorenz system [1] in 1963, the chaos theory has become a hot spot of nonlinear field research. Most of the researches on weak signals based on chaos theory use a single chaotic system for detection. To improve the chaotic system complexity and the accuracy of signal detection, this paper proposes a new hidden attractor coupled chaotic system. Eoretical analysis indicates that the system is sensitive to initial values and immune to noise, and the coupled chaotic system is applied to weak signal detection. Rough data analysis and experimental data, the system proposed in this paper can detect signals sized 1 × 10− 6, and the signal-to-noise ratio reaches −73.892 dB. The immune signal reached the order of 3.5 × 10− 3, and the error range of the initial phase angle is ± 0.09. erefore, the detection performance of the coupled system proposed in this paper is better than the single chaotic system proposed in [45, 46, 53,54,55]
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