Stability Analysis Of Markovian Stochastic Neural Networks With Time Delays

Neural networks have been widely used in many pratical engineering such as signaltransmission, image processing, pattern recognition, automatic control, associativememory, combinatorial optimization, etc. Therefore, something about the characteristicsof neural networks state received more and more attention from researchers. The stability,a feature of network state dynamics, is the prerequisites that neural networks must to meetand can be applied to practical engineering, and it is also one of the important issues manyscholars researched. In this thesis, the exponential stability for a class of Markovianstochastic neural networks with mixed time delays and stability analysis of periodicsolution for memristor-based neural networks with impulses are considered. The mainresults are as follows:(1) The Markovian stochastic neural networks with mixed time delays and inverseH o l deractivation functions is established. By applying brouwer degree properties, theexistence and uniqueness of the equilibrium point for Markovian stochastic neuralnetworks have been proofed, based on LMI approach, a sufficient condition has beenachieved to ensure the Markovian stochastic neural networks to be exponential stability.(2) The interval Markovian neural networks with mixed time delays and stochasticdisturbance is introduced. By structuring the Lyapunov-Krasovskii functional andapplying linear matrix inequality (LMI) techniques, some sufficient conditions have beenachieved to ensure the neural networks to be exponential stability. Finally, two numericalexamples are provided to illustrate the validity of the theoretical results.(3) The memristor-based neural networks with impulses is presented. Under theinfluence of impulses, by using the Leray-Schauder alternative theorem, the existence ofperiodic solution for this memristor-based neural networks is investigated. By emplytingthe definition of matrix measure, a sufficient condition which ensures the uniqueness andglobal exponential stability of the periodic solution is given.