Chaotic Dynamics of a Linear Chain of Periodically Stimulated Neurons with Random Synaptic Connections

Dynamics of a neural network in the form of a linear chain of artificial neurons S$\text{}_{i}$∈(-1,1) influenced by an external sinusoidal stimulation is investigated as a function of the range k of synaptic connections with random values. Time evolution of the network is periodic for small k, however, clusters of neurons oscillating with a triple period of external stimulation, with quasiperiodic or with chaotic time evolution may occur. For increasing k the number and width of the chaotic clusters increase and for k >4 the chaotic motion occurs in the whole network. A route to chaos in the considered system is discussed.