The periodic window is researched by means of the symbolic dynamics and formal language. Firstly, the proper sampling period is taken and the orbital points of periodic motion are obtained through Poincar6 mapping. Se...The periodic window is researched by means of the symbolic dynamics and formal language. Firstly, the proper sampling period is taken and the orbital points of periodic motion are obtained through Poincar6 mapping. Secondly, according to the method of symbolic dynamics of one-dimensional discrete mapping, the symbolic sequence describing the periodic orbit is obtained. Finally, based on the symbolic sequence, the corresponding model of minimal finite automation is constructed and the entropy is obtained by calculating the maximal eigenvalue of Stefan matrix. The results show that the orbits in periodic windows can be strictly marked by using the method of symbolic dynamics, thus a foundation for control of switching between target orbits is provided.展开更多
Neural firing patterns are investigated by using symbolic dynamics. Bifurcation behaviour of the Hindmarsh-Rose （HR） neuronal model is simulated with the external stimuli gradually decreasing, and various firing act...Neural firing patterns are investigated by using symbolic dynamics. Bifurcation behaviour of the Hindmarsh-Rose （HR） neuronal model is simulated with the external stimuli gradually decreasing, and various firing activities with different topological structures are orderly numbered. Through constructing first-return maps of interspike intervals, all firing patterns are described and identified by symbolic expressions. On the basis of ordering rules of symbolic sequences, the corresponding relation between parameters and firing patterns is established, which will be helpful for encoding neural information. Moreover, using the operation rule of ＊ product, generation mechanisms and intrinsic configurations of periodic patterns can be distinguished in detail. Results show that the symbolic approach is a powerful tool to study neural firing activities. In particular, such a coarse-grained way can be generalized in neural electropt/ysiological experiments to extract much valuable information from complicated experimental data.展开更多
Using the high sensitivity to initial values of chaotic systems, this paper describes an application of chaos in the field of measurement. A general method for signal coding based on symbolic sequences and the relatio...Using the high sensitivity to initial values of chaotic systems, this paper describes an application of chaos in the field of measurement. A general method for signal coding based on symbolic sequences and the relationship between the variable (to be measured) and its symbolic sequence are presented. Some performances of the chaos based measurement system are also discussed. Theoretical analysis and experimental results show that chaotic systems are potentially attractive in the field of measurement.展开更多
基金This project is supported by National Natural Science Foundation of China(No.50075070).
文摘The periodic window is researched by means of the symbolic dynamics and formal language. Firstly, the proper sampling period is taken and the orbital points of periodic motion are obtained through Poincar6 mapping. Secondly, according to the method of symbolic dynamics of one-dimensional discrete mapping, the symbolic sequence describing the periodic orbit is obtained. Finally, based on the symbolic sequence, the corresponding model of minimal finite automation is constructed and the entropy is obtained by calculating the maximal eigenvalue of Stefan matrix. The results show that the orbits in periodic windows can be strictly marked by using the method of symbolic dynamics, thus a foundation for control of switching between target orbits is provided.
文摘Neural firing patterns are investigated by using symbolic dynamics. Bifurcation behaviour of the Hindmarsh-Rose （HR） neuronal model is simulated with the external stimuli gradually decreasing, and various firing activities with different topological structures are orderly numbered. Through constructing first-return maps of interspike intervals, all firing patterns are described and identified by symbolic expressions. On the basis of ordering rules of symbolic sequences, the corresponding relation between parameters and firing patterns is established, which will be helpful for encoding neural information. Moreover, using the operation rule of ＊ product, generation mechanisms and intrinsic configurations of periodic patterns can be distinguished in detail. Results show that the symbolic approach is a powerful tool to study neural firing activities. In particular, such a coarse-grained way can be generalized in neural electropt/ysiological experiments to extract much valuable information from complicated experimental data.
文摘Using the high sensitivity to initial values of chaotic systems, this paper describes an application of chaos in the field of measurement. A general method for signal coding based on symbolic sequences and the relationship between the variable (to be measured) and its symbolic sequence are presented. Some performances of the chaos based measurement system are also discussed. Theoretical analysis and experimental results show that chaotic systems are potentially attractive in the field of measurement.
