Bounds on the Period of Oscillatory Activity in Randomly Interconnected Networks of Neuron-Like Elements

Abstract—Repetitious activity is assumed in randomly interconnected networks of elements with spacial and temporal summation of input excitation and exponentially decaying threshold and stimulation. Bounds on the period of that oscillatory activity are theoretically established, and verified by computer simulation. The dependency of such bounds on threshold and stimulation decay rates, number of inputs to each element, maximum and return values of threshold, the presence of inhibitory elements in a network, and the profile of network activity is shown.