Dynamical Property Analysis For Chaos System Used To Detect Weak Signal

The purpose of weak signal detection is testing the useful signal from high noise background. Therefore it desperately needs to develop science and technology. Although the traditional measure methods are useful to detect weak signal which is relative to the small noise, it is difficult to do it. In recent years, a new development direction, using theory of chaos to detect signal, has been formed in signal processing field The reason why chaos system is used to detect weak signal is that it is sensitive to initial conditions and can suppress noise.In order to effectively extract weak signal from noisy background, this paper improved fractional van der pol equation and a new chaotic system. They were used to detecting the amplitude and frequency of weak signals. Firstly, the stability of van der pol system was analyzed briefly. Then based on theory of fractional system, this paper analyzed the stability of fractional coupled van der pol equation. The conclusion was proved to be right by Matlab. This paper studied the property of fractional van der pol equation by simulating used Simulink. Whether the fractional van der pol system is chaotic or not, we can judge it by observing the figures. When the system was in critical state, a weak signal with noise was input into the system. The phase of system had a big change. When the system was in critical state again, we could get the amplitude by comparing two critical values. Finally, a new chaotic system was introduced. The stability of the new chaotic system was analyzed. Controlling chaos is hot in resent years. Two methods, proportional differential control and time-delayed feedback, were used to control the new chaotic system. The conclusions were proved to be right by Matlab. When the system was in critical state, a weak signal with noise was input into the system. The phase of system had a big change. When the system was in critical state again, the frequency spectrum map was given. The frequency of weak signal was known by the frequency spectrum map.