Nonlinear resonances and multi-stability in simple neural circuits

This article describes a numerical procedure designed to tune the parameters of periodically driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic solutions available to the system within a range of the parameters that define the driving. The procedure is applied to a problem of interest in computational neuroscience: a circuit composed of two interacting populations of neurons under external periodic forcing. Depending on the parameters that define the circuit, such as the weights of the connections between the populations, the response of the circuit to the driving can be strikingly rich and diverse. The procedure is employed to find circuits that, when driven by external input, exhibit multiple stable patterns of periodic activity organized in complex tuning diagrams and signatures of low dimensional chaos.