Weak Signal Detection Based On Duffing Oscillator

An important application of Chaos theory in information science is information detection. Chaos system is sensitive to weak signals and immune to noise, which make chaos have good prospects in information detection technique. Chaotic oscillator detection for weak signals belongs to this technique. Although it is a new subject, it has already made a great progress. There are two kinds of methods in detection for weak signals based on chaos: one is based on phase transition of the chaotic system, when its parameter stay in the critical value, the other is to use some characteristic exponent of the system. Both the two weak signal detection methods under strong noise are all depend on the property of the system at the critical value. Study and solvent about the problems in these two methods were made in this paper. Phase transition of chaotic systems is widely used in chaotic oscillator detection method. The main target of this method is to improve the detection limits, get better noise suppression and enlarge the scale of objects to be detected. So it is necessary to find a much better detection model and analyze the dynamical behavior and noise suppression ability to improve the precision and detection limits. Nowadays, Single Duffing Oscillator (SDO) was widely used as the detection system, but the state of the system sometimes is unstable at the critical point when it is affected by strong noise, so some modification should be made. In this paper we present a Coupled Duffing Oscillators (CDO), according to the general study of single Duffing oscillator, as our detection system for weak signal detection, and improve the stability and detection property of the system at critical point. For practical application, we use the CDO to realize the detection of inphase axis of seismic event in seismic exploration. According to our research it is possible to use the chaotic system to carry out the detection. Floquet exponent and Lyapunov exponent are two very important characteristic exponents in the judgment of nonlinear dynamical system behavior. Lyapunov exponent was widely used as the identification of the chaotic or non-chaotic states of the nonlinear system, while according to its definition, great calculation should be carry out to get its real value. For the Floquet exponent, it is seldom used in the identification of chaotic systems, but when the system enters into the great periodic state from chaotic state, Floquet exponent can quantificationally describe the behavior of the system. It need lower observation and calculation, so it is suitable to choose the Floquet exponent as the tool to realize the estimation of the parameter of weak signal. In particular, if we can find the relationship between the Floquet exponent and the parameter of signal, then the estimation can be achieved. According to the analysis above, we determine the main work of this paper as follows. Firstly, find a new chaotic oscillator for weak signal detection, which should have better noise suppression ability, and then we should analyze the dynamical behavior, threshold and detection limit of this system. Secondly, take some characteristic exponents (Floquet exponent in this paper) in the weak signal detection method; study the curve of the exponent and the parameter of signal and realize the estimation in weak signal detection. The following gives the main work of this paper in detail. 1. Study of identification methods of system behavior Make an analysis of the existed methods for system behavior identification method, and classify these methods into two categories: visual methods and quantitative methods. Visual methods include time evolvement of the system's variable , phase trajectory map, frequency flash sampling, Poincarésection andpower spectrum. Quantitative methods include fractal dimension, Kolmogorov entropy, Lyapunov exponent and Floquet exponent. Then we used mathematical model to compare these methods, and got a conclusion: Although the visual methods sometimes have error, and even can't accurately judge the system's state when the noise is very strong, they are very convenient to use and operate and have clear physical meaning. While the quantitative methods judge the system's state by explicit numerical values, they are more accurate. Furthermore, Lyapunov exponent method is the most basic and also the most important method among them; With respect to the Floquet exponent, it should be used when the system stay in the great periodic state, although it is seldom used in identification of the state of chaotic system. 2. Analysis of Coupled Duffing Oscillators system Firstly, we analyze the dynamical behavior of single Duffing oscillator. Because of the similarity between the SDO and CDO, it is beneficial to analyze the SDO; And then, according to the dynamical behavior of CDO,study their use in the weak signal detection method. At last, we get the conclusion: CDO has better stability and detection ability than single oscillator by simulation experiment. 3. Coupled Duffing oscillator in chaos detection for weak signals At first, we use experiment method to find the threshold of CDO, and then such system can be used as the detection system. Secondly, Coupled Duffing oscillator was used as the detection system to detect the sinusoid signal and other kinds of periodic signals. From the simulation study, we can see better noise suppression and signal detection ability can be achieved if we use the CDO as our detection system. 4. Weak signal detection method based on Floquet Exponent A study on chaotic oscillator for weak signal detection method based on Floquet...