Chaos characteristics analysis of transient signals for phase-locked synthesizer based FHC system

Frequency synthesizer plays an important role in frequency hopping communication system. In this paper, we derivate the conditions for a system to become the chaotic based on the phase model of phase-locked synthesizer. We found that the system parameter changing during the frequency switching is able to make the system to be chaotic. Based on the Cao´s method [5], we find that the fractal dimension of the transient signals should be equal to or less than 4, which also provides the maximal positive Lyapunov exponent. In addition, the unique double-ring attractor of them is also reproduced through the phase reconstruction, which also implies that the frequency switching will result in a chaotic for Frequency-Hopping Communication system.