| In this thesis, the complex-valued recurrent neural network models are presented and their dynamical behaviors, including global stability and periodic oscillation, multistability and multiperiodicity, are studied. Some simulation results are given to illustrate the obtained results and an application on complex-valued associative memory is provided.;As an extension of the real-valued recurrent neural networks, the states, connection weights and activation functions of complex-valued recurrent neural networks are complex-valued. It can deal with complex-valued signals and greatly improve the capability of solving some problems than the real-valued recurrent neural networks. In recent years, complex-valued recurrent neural networks have been widely applied and studied in machine learning, engineering optimization, image processing, pattern recognition, etc.;As is well known, the analysis and application of recurrent neural networks rely crucially on the equilibrium points or periodic orbits of the neural networks. This thesis focuses on the dynamical behaviors of complex-valued recurrent neural networks. The activation functions plays an important role in the dynamical behaviors of recurrent neural networks. In the complex domain, there are various types of activation functions with different properties from those in the real domain, which results in different dynamical behaviors of the complex-valued recurrent neural networks. In this thesis we mainly consider two types of complex-valued activation functions. For different types of activation functions, we use different approaches to analyze the dynamical behaviors of the relevant neural networks.;We first analyze the global stability and periodicity of the complex-valued recurrent neural networks. By using Lyapunov approach and the techniques of M-matrix and linear matrix inequality (LMI), we obtain the existence and uniqueness condition of the complex-valued recurrent neural networks and the sufficient conditions of the global stability and exponential periodicity of the neural networks. Next, we study a complex-valued recurrent neural network with one step piecewise linear activation functions and obtain the sufficient conditions of the mulistability and multistability of the neural networks. Finally, we use the discretization technique to obtain the discrete-time analogue of continuous-time complex-valued recurrent neural network models and study its dynamical behaviors by using discrete-time Lyapunov function and difference method. |
