Linear Congruential Sequences: Feedback and Recurrent Neural Networks

In this research paper, state space representation of a non-linear dynamical system associated with a linear congruential sequence is discussed. Based on the periodicity of such sequence, it is inferred that the dynamical system exhibits cycles in the state space. The cycle length is determined. A novel model of neuron, called “modulo” neuron is proposed. Based on such a neuron, an associative memory and certain recurrent neural networks are proposed.