Artificial neural networks emerged in the early 1940s as a connectionist approach to modeling the behavior of interconnected living nerve cells within the intricate cognitive framework of the brain. Over the years, this idea has undergone unprecedented proliferation of ever-expanding application areas, accompanied by an exponential surge in the mathematical formalism employed. This prodigious growth poses severe demands on computational hardware infrastructure. The current research suggests a novel approach for optimizing artificial neural network architectures using resource-sharing techniques. It is discussed the concept of merging context-switching and time-division multiplexing in building a single-neuron artificial neural network with the aid of an FPGA device. This would benefit the significant reduction of hardware resources and the possibility of creating small yet very efficient artificial neural networks without deteriorating the dynamical system performance.