Weak Signal Detection By Fractional Order Chaotic System

Chaos theory, as a frontier of research, from original exploration to graduallyimprovement of theory, has been applied in many fields such as engineering andscience. Because of the noise immunity and sensitivity to the periodic signals, weaksignal detection by use of chaotic system has broad prospects for development.People found that the fractional order chaotic systems,which have more complexdynamic behaviors, can more accurately describe the phenomenon than integer orderchaotic systems in some fields, This thesis will introduce fractional order chaoticsystems to detect the amplitude and the frequency of weak signal.In this thesis, the research mainly includes the following aspects:1. Fractional order chaotic system and Simulink simulation method are introduced.Fractional order Duffing system which is used in detecting amplitude in the weaksignal, verify that fractional order Duffing system is better than integer order Duffingsystem on anti-noise performance under the same experimental conditions.2. By using the theory of chaos control, we use fractional order Jerk system to detectthe frequency of weak signal. On the basis of the theory of proportional differentialcontrol, we can perfectly control the fractional order Jerk system, finally perfectlydetect the frequency of weak signal drown in strong noise.