Much of the current interest in artificial neural networks stems not only from their richness as a theoretical model of collective dynamics but also from the promise they have shown as a practical tool for performing parallel computation. Theoretical understanding of neural network dynamics has advanced greatly in the past two decades. In particular, the growing use of continuous-time recurrent neural networks, both in the theoretical and applied areas of computer science, has led to a growing need for a comprehensive understanding of the dynamic properties of neural networks in general. For example, it is important to understand what kinds of dynamic behavior a given network can exhibit, or how a network's dynamic behavior depends on its parameters, to name just a couple of important questions. We are certain that even partial answers to these and other questions would contribute significantly to our understanding of existing networks, and could help to guide the synthesis of new networks for solving particular problems. In this context, there has been a recent upsurge of interest in isolated - (single) or few - neuron nonlinear dynamics. In particular, it has been shown that simple neuron models involving one or two threshold switching elements, added with inertial terms, exhibit a complicated bifurcation behavior including chaos [1].This result, among others, stems from the commonly held belief, especially among physicists, that simple models involving a few degrees of freedom can frequently describe, quite accurately indeed, the dynamics of very complex systems. In this sense, it has been shown that the dynamics of a single neuron is obtained from a network of symmetrically interconnected neurons through the procedure of adiabatic elimination, that is, through the separation of time scales [2].Similarly, but from a computational point of view, it is believed that some properties of larger networks can be deduced from the dynamics of simple networks. In this respect, it is obvious that the dynamics of a single isolated neuron and of a neuron with a self-connection, or autosynaptic neuron, are the basic building blocks from any larger network [3].Now, one of the most interesting problems in neural dynamics is to understand why some kinds of connected networks have the ability to store temporary information; this problem is known as the time representation problem. In order to solve it, one line of research takes into account the results of biological investigations where it appears that the time representation problem involves a (maybe adaptive) short-term memory mechanism in the neural network. On the other hand, different researches believe that hysteresis effects could give rise to short-term memory phenomena [4].The hysteresis effect, in turn, is believed to be caused by the presence of multi-stable states in the neural population. However, multi-stable dynamics do not appear only in large neural populations. In fact, single neuron models including self-interactions or complex activity functions may exhibit multi-stable levels of activity. We had shown that a simple neuron model with a piece-wise linear activity function and an axonal delay is capable to generate hysteresis responses even if it has no self-interaction [5].We also showed that the hysteresis response of our model is due to a phase lag between the external input and the neuron's response and that this behavior is neither an artifact of the discontinuity of the activity function nor it is caused solely by the presence of the axonal delay. We also showed that the hysteresis effect could be modulated by the external signal and by the neuronal parameters and this modulation could be used to process complex signals.In the work we extend our previous investigation and study the dynamic behavior of a simple neuronal circuit formed by a single neuron with an autosynapsis, that is, a neuron that has its own output feedbacked as one of its input signals. Additionally, we relate the neural dynamics to short - term memory phenomena. Our neuron model is built with three elementary neuronal operations, two linear and one non-linear. The two linear operations mimic the dendritic and somatic operations found in the biological neurons, meanwhile the non-linear operation or activity function mimics the axonic and terminal operations of the neuron.