Periodic orbits on discrete dynamical systems

In this paper, we discuss the discrete dynamical system Xn+1 = betax(n) - g(x(n)), n = 0, 1,..., arising as a discrete-time network of single neuron, where beta is the internal decay rate, g is a signal function. First, we consider the case where g is of McCulloch-Pitts nonlinearity. Periodic orbits are discussed according to different range of beta. Moreover, we can construct periodic orbits. Then, we consider the case where g is a sigmoid function. Sufficient conditions are obtained for (*) has periodic orbits of arbitrary periods and an example is also given to illustrate the theorem. (C) 2003 Elsevier Science Ltd. All rights reserved.