| In this thesis, the dynamic behaviors of solutions are considered for the following excited neural network model of two neurons with piecewise constant argument signal transmission function:and excite-frustrated neural network model of two neurons with piecewise constant argument signal transmission function:where, x(t) and y(t) denote the activation of two neurons, the constant μ > 0 is the decay rate, the constants τ1 > 0 and τ2 > 0 are the synaptic transmission delays, [u]+ = 0.5(|u| + u), g : R→ R is the activation function given byin which, λ > 0 is the exciting constant, 0 < a < b are the given constants, [a, b] represents the responding interval of neurons. By the technique of analysis, we study the convergence of solutions and the existence of periodic solutions, and find that such networks have some interesting dynamic behaviors. It is consists of four chapters.As the introduction, in Chapter 1, the background and history of artificial neural networks are briefly addressed, and some notations and definitions are given in this chapter. In Chapter 2, we study carefully the dynamic behaviors of the model without delay, the convergence of solutions is proved for some fields of initial functions, and two fields D1 and D2 are given, we find that every solution with initial value Φ = (φ,ψ) ∈ IntD1 ∪ IntD2 is eventually periodic. Furthermore, we give the attractive basins of the origin O. In Chapter 3, the dynamic behaviors of synchronized solutions are discussed for the excited model with delay τi> 0(i = 1,2), some interesting results are given for the convergence of solutions and the existence of periodic solutions. In Chapter 4, we consider the convergence of insynchronized solutions of the excited model and solutions of the excite-frustrated model, some interesting results are established. Our results show that the delays play important roles in the influence to the dynamic behaviors of solutions of such two classes of neural network models.
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