Entrainment control in a noisy neural system

The open-plus-closed-loop (OPCL) entrainment control put forth by Jackson and Grosu [Physica D 85, 1 (1995)] is applied to an effective-neuron system as a way to extract stable limit cycles from a chaotic attractor, analogous to the retrieval of memories from a memory searching state. Additive Gaussian white noise, representing the natural noise inherent in any real dynamical system, is added to the entrainment control mechanism. Moderate levels of additive noise have little effect on successful entrainment, as reflected in phase-space plots and Lyapunov exponents. All three Lyapunov exponents are negative, which suggests parallels between OPCL control and chaotic synchronization.