Abstract :
Consider the difference equation
xn+1 = βxn − g(xn), n = 0, 1, . . . , (∗)
arising as a discrete-time network of single neuron, where β is the internal decay rate, g is a signal
function with McCulloch–Pitts nonlinearity. For any positive integers k and m, necessary and sufficient
conditions are obtained for (∗) has a periodic solution of period 2k + 1 or 2m. In addition,
sufficient conditions are also given for (∗) has a (2k + 1)2m-periodic solution.
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