| A wide variety of natural phenomena exhibit complicated, unpredictable and seemingly random behavior. Chaotic dynamics appears to provide a relatively simple and possibly more satisfactory explanation to a lot of complicated phenomena among them. Chaos theory shows that simple deterministic systems with only a few variables can generate seemingly random behavior.The purpose of chaotic theory is discovering possible simple rules, which hide in the seeming random phenomena and obtaining common rules which a big group of complicated problems follow. With chaotic dynamics developing, predicted complexity of time series have been profoundly comprehended. Even if it is impossible that long-term approximate prediction for chaotic behaviors, but it is possible that accurate short-term prediction for it. So studying prediction of chaotic time series probably solve a lot of complicated problems. In addition, chaotic theory provided different characteristic parameters describe chaotic time series and communication signal is also a sort of nonlinear time series, so difference of modulation types of communication signal is embodied by difference of time series. This dissertation studys prediction of chaotic time series and chaotic application in the aspect of recognition of communication signals. Main contents studied include: (1) nonlinear adaptive filter predicting chaotic time series and hopping frequency code;(2) common used neural networks (Backpropagation neural networks and radial basis function neural networks) modeling and predicting chaotic time series and hopping frequency code;(3) a fast method of predicting chaotic time series;(4)feature extraction of communication signals based chaotic theory;(5) classifier design based fuzzy integral.Several value and important results which bring forth new ideas areachieved and listed as following: 1. Studying convergence of two-rank volterra adaptive filtersAs predicting performance of volterra adaptive filters mainly depending on adaptive algorithm and convergence of adaptive filters is important criterion evaluating adaptive algorithm good or bad, we have studied convergent relationship between a control parameter and predicting error, between coefficient of initial filters and predicting error, among coefficient of filters, between predicting error and coefficient of filters and between ranks of filters and coefficient of filters.2. Determined ranks of nonlinear adaptive filters.As ranks of nonlinear adaptive filters based nonlinear adaptive technology is determined arbitrarily by people, ranks of filters not only influence predicting accurateness of time series, but also involve computing complexity of realizing this kind of filters. Via theory analyzing and experiments, optimal input dimensions of nonlinear adaptive filters is obtained, at the same time it is presented a simple algorithm which determine optimal input dimensions of nonlinear adaptive filters.3. In order to meet engineering demands of real time, a fast method predicting chaotic time series is proposed.As hopfield neural networks have many advantages such as fast convergence, software or hardware realizing hopfield neural networks, it is presented that fast predicting method based hopfield neural networks, which combines volterra predicting filters and hopfield neural networks. This method provides a solution to real time engineering problems.4. Analysis of dynamic characteristics of hopping frequency codes Hopping frequency codes are pseudo-random sequences generatedby determinate rules. It is seemingly random the same as chaotic sequences. It is studied that dynamic characteristics(Correlation dimension and largest Lyapunov exponents )of some kind of FH codes (m sequences, RS sequences, Nonlinear sequences and chaotic sequences) by dynamic system method,the results show that FH codes are of chaotic characteristics5. Predicting performance has been studied for hopping frequency codes by a kind of method predicting chaotic time series via chaotic theory...
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