Research And Applications Of New Features For Chaos Recognition

Chaotic dynamics bridges the gap between deterministic and stochastic theory.Chaos recognition is a fast measure of the computability and complexity of multivariate hypotheses for finite-length datas.Its essence is to distinguish the chaotic signals from the periodic signals and random signals through the geometrical or numerical statistics.One of the most difficult problems in the field of complexity measure is how to recognize the chaotic signals quickly and accurately.Firstly,this dissertation introduces the basic theory of chaos.Then,it explains the mainstream recognition methods such as Lyapunov exponent,0-1 test for chaos and C0 complexity for details,followed by comparing the advantages and disadvantages of these methods.Secondly,different threshold functions with golden ratio are used to compress the signals nonlinearly,which produces a new sequence called "s variable".Referring to the identification principle of 0-1 test for chaos,we can identify the states of the signals quickly by observing the map of the integral sequence of s variable and calculating the progressive growth rate of the integral sequence of modulated s variable.Taking classic chaotic equations and circuits as examples,the effectiveness of the new algorithm has been verified by comparing it with three kinds of chaotic recognition methods.Thirdly,we tested and analyzed the anti-noise performance of the new algorithm,the result shows that the 3S map can recognize the periodic signals with 34%noise(uniform random noise)and the chaotic signals with 10%noise(uniform random noise).Ks value can recognize the periodic signals with about 8%noise(Gaussian noise).Therefore,we have proved that the new algorithm has better anti-noise performance than 0-1 test for chaos.Finally,we applied the new compression features to analyze the characteristics of voice signals and to identify the states of the new chaotic circuits.The result shows that the voice signals have chaotic features and the new algorithm is suitable for recognizing the states of the actual circuits.The main idea of this dissertation is to nonlinearly compress the time series with different threshold functions.We have constructed the "s variable" successfully and proposed new compression features(including 3S map and Ks value)which can be used to recognize chaos.Also,the anti-noise performance of the new algorithm has been improved.At the end of the dissertation,the applications of the new algorithm were dicussed.