With Binary Feedback And Continuous Signal Transmission Function Of Time Delay Neural Network Model Dynamics

This thesis discusses two kinds of self-feedback artificial neural networks of twoneurons:Here x(t) and y(t) describes separately the active states when the two neurons are at the exact time of t, r > 0 is the synaptic transmission delay, f and g are the signal functions:a 0 and b 0 are two given constants. and 02 are threshold constants and .This thesis is composed of two chapters. The first chapter deals with one kind of two-neuron neural networks with positive self-feedback coefficient. In chapter 2, we discuss the simular system with negative self-feedback coefficient.As the discontinuity of / and g makes it difficult to apply directly the existing results of dynamic system to system (I) , (II). we use the iterative method of one-dimensional function and reduction to absurdity to make clear our models. The results show that, when and 02 are in various intervals, the trajectories for systems (I) are either ultimately periodic or convergent to an equilibrium. The difference between system (I) and system (II) only lies on the sign of self-feedback coefficient, but their asymptotic behavior of trajectories are much different. For the given initial value, the solutions for system (II) all converge to the certain equilibrium.For system (I), we also verify some results through numerical simulation.