Chaos Weak Signal Detection Methods

Chaotic motion, which widely exists, can describe the very typical behavior of many nonlinear systems. Chaos has been paid wide attention because of its some good intrinsic properties, and it has been widely and successfully applied to many areas. Chaotic oscillator detection for weak signal belongs to an important application of Chaos theory in information science, chaos system is sensitive to weak signals and immune to noise, which make chaos have good prospects and a great progress in signal detection technique. There are two kinds of methods in detection for weak signals based on chaos: one is based on phase transition of the chaotic system, the other is to use some characteristic exponent of the system. Both the two weak signal detection methods are dependent on the property of the system at the critical value. In this paper, we combine these two methods together to detection weak signals under strong noise. The following gives the main work of this paper in detail.1. Melnikov method and Lyapunov characteristic exponent under period state is used to determine the critical value of the chaos detection systemOne method is that we have presented an analytical computation based on the core thought of Melnikov method, and have inferred the range of driving value under chaotic state, so we can determine the critical value of which system enters into the chaotic state.The other is that on the relation between critical value and structure stability, we have presented the basic thought of determining the critical threshold value of the detection system by the Lyapunov characteristic exponent under period state and simulation results with Duffing detector verified the feasibility. Compared with the experimental technique, the Lyapunov characteristic exponent method is more accurate and more efficient.2. Duffing oscillator in chaos detection for weak signalsFirstly, we analyze the dynamical behavior of Duffing oscillator, and study their use in weak signal detection method. Then such system which is in the critical state of chaos can be used as the detection system to detect weak sinusoid signal, including single sinusoid signal, multiple sinusoid signal and unknown frequency of sinusoid signal. First present a new measurement method of frequency when the frequencies of multiple signals are close to, the results of experiments show that above method has many merits such as simple, effective, easy to be applied.