Periodicity Of A Discrete Time Bipolar Artificial Neural Network

There are nearly 1011 neurons in human beings.Men facilitate reading and thinking under the highly in termination and operation of the neurons.Some of neural structure arecongeni-tal.Other parts have been established by experience.Each of biological neurons can be seen as a rich assembly of a microprocessor. It is generally understood that all biological neural functions are stored in the neurons and in the connections between them.For instance learning is viewed as the establishment of new connections between neurons or the modification of existing connections.The neurons that we consider here are not biological.They are extremely simple abstracted and called artificial biological neurons.Networks of these artificial neurons do not have a fraction of the power of the human brain,but they can be trained to perform useful functions.In this paper,we study the period of the bipolar artificial neural network with discrete time.One such simple artificial neural network model consisting of 4 neurons situated on the vertices of a regular Tetrahedron with 4 vertices,and are connected by its edges.The systematic behaviour with the discrete time and before the moment depends on the state of the system.The status change of neurons can be described by differential system as follows:The weight matrix and the bias are dependent on two parameters α and β. Furthermore,each neuron unit can take on two values designated by+land-1.This study is a two-dimensional neurons, different from the previous one-dimensional neurons, so the analysis is more compli-cated.A discrete time bipolar neural network depending on two parameters is studied. It is observed that it’s dynamical behaviors can be classified into thirty-six cases. For each case, the long time behaviors can be summarized in terms of fixed points, periodic points, basin of attractions. Due to the symmetry of the tetrahedron, the discussion is divided into 21 categories.Through analysis of the parameters and neural network, we can get a completed periodic conclusion.