Synchronization Of Chaotic Sequence Denoising And Nonlinear Systems

As an important part of nonlinear science, chaos has generated a huge influence to modern science and technologies. It brings new ideas to promote the further development of signal processing and communication. It also has broad application. This thesis developed a study about nonlinear denoising method of chaotic sequence and the synchronization of nonlinear dynamic systems. The main contens and results of this thesis are:1,An algorithm based on singular spectrum analysis for denoising of chaotic sequence was studied. The basic principles of this method were expounded. The effects on the final denoising result which brought by main component truncation were discussed. Usint the difference of the signal and noise singular spectrum, the method of determined the order of optimal reconstruction was proposed. The limitation in application of this method was analysed. And the research indicated that it didn't apply to chaotic signal which had constant spectrum.2,The locally projective noise reduction was studied. The factors influenced denoising result of this method was analysed. The two aspects were studied in detail. Considering different neighborhood ought to possess different local characteristic and each neighor should correspond to different optimal radius, we utilized an adaptive algorithm to choose the size of each neighbor, and each neighbor could have its optimal radius. Considering the false neighborhood point could decline the denoising performance, an improved neighborhood selection method combing with the singulai spectrum analysis technique was studied, and principal component was chosen to reconstruct a less noisy phase space. Using this method, the accuracy of the selected neighbors was elewated effectively.3,In this paper, we suggested an anticipating projective response scheme in coupled dynamical systems, from which a large class of different drive-response systems could be constructed by choosing different functions and changing the scaling factor. A specific case of the scheme which was named the accelerative anticipating projective response scheme was studied in detail. In this specific scheme, the amplitudes of the drive and response systems synchronized up to a scaling factor and the response system evolved with a faster speed. Further, the robustness of this scheme was proved under the existence of the small disturbance of the driving term, interference of the driving signal and parameter mismatches.