Dynamics Research Of Neural Network Models With Continuous Or Discontinuous Output Functions

In this thesis, the dynamic behaviors are addressed for both the so-called improved signal range model of cellular neural networks and several classes of neural networks with discontinuous neuron activations.In Chapter One, the history and development of neural networks are briefly intro-ducted. The background and motivations of this work are also given in this chapter.In Chapter Two, we list some basic definitions and lemmas concerning with matrix theory, set-valued analysis and differential inclusion.In Chapter Three, the equilibrium points of a class of improved signal range cellular neural networks described by invariant cloning templates are considered. Comparing to the standard delayed cellular neural networks, the output functions of improved models are allowed to be unbounded, which results that the improved models have the features such as lower power consumption, greater cell density and running faster. This chapter firstly address the global attractive set and positive invariant set to make sure of the general potential domains of equilibrium points. Secondly, according to the invariability of state feedback templete and delay feedback templete, the existence, number and local asymptotic stability of equilibrium points are studied in each saturation region by constructing the suitable iterative mapping. Finally, one sufficient condition is obtain to ensure the global exponential stability of this system, and the explicit existing region of the unique equilibrium point is further located. The obtained results extend previous works on above issues of standard delayed cellular neural networks.In Chapter Four, the dynamics of a class of recurrent neural networks are investigated, where the neural activations are modeled by discontinuous functions. The moldels studied in this chapter includes the known Hopfield neural network models. Without presuming the boundedness of activation functions, we establish some sufficient conditions to ensure the existence, uniqueness, global exponential stability of state equilibrium point and global convergence of output equilibrium point, respectively. Furthermore, under certain conditions, we prove that this system is convergent globally in finite time, which is a special character of neural networks described by differential equations with discontinuous right hand. The analysis is based on the properties of M-matrix, Leray-Schauderfixed point theorem of multivalued version and generalized Lyapunov-like approach.Chapter Five addresses a class of delayed neural networks with discontinuous neu- ron activations. Some sufficient conditions to ensure the existence and global asymptotic stability of the state equilibrium point are presented. Furthermore, the global convergence of the output solutions are also discussed. The assumptive conditions imposed on activation functions are allowed to be unbounded and nonmonotonic, and the restrained conditions on connection weigh matrix are less than previews works on the discontinuous or continuous neural networks.In Chapter Six, we consider a class of discontinuous recurrent neural network models described as a periodic differential system. Without presuming the activation functions to be continuous, bounded and monotone nondecreasing, by utilizing linear matrix inequality, Cellina approximate selection theory in differential inclusion and the uniform convergence Theorem ofδ-solutions in differential equations with discontinuous right hand, a sufficient condition is provided to ensure the existence of periodic solutions of this system. The global exponential stability of periodic solution is also proven by employing the generalized Lyapunov-like approach.