Analysis Of Dynamic Behavior Of Delayed Neural Networks Models

In this thesis, the dynamic behaviors of solutions are considered for the following three kinds of neural network models: two-neuron networka ring of neurons networkand a class of Hopfield neural network with distributed delayswhere, n corresponds to the number of neurons in a neural network; X_i(t) denotes the potential (or voltage) of neuron i at time t; f_i(·) denotes a non-linear output function; I_i(t) denotes the ith component of an external input source introduced from outside the network to neuron i at time t; a_i(t) denotes the rate with which neuron i resets its potential to the resting state when isolated from other cells and inputs at time t; b_ij(t) denotes the strengths of connectivity between neuron i and j at time t respectively; τ_ij(t)corresponds to the time delay required in processing and transmitting a signal from the jth neuron to the ith neuron at time t. A set of stability, periodic and almost periodic oscillation results for such neural networks models are derived by employing Brouwer's fixed point theorem, inequality analysis and a continuation theorem of the coincidence degree.