Abstract
Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support functions such as breathing and locomotion. There is also substantial evidence that the brain encodes memories and processes information via sequences of neural activity. Traditionally, rhythmic activity and pattern generation have been modeled using coupled oscillators, whereas input classification and pattern completion have been modeled using attractor neural networks. Here, we present a theoretical framework that demonstrates how attractor-based networks can also generate diverse rhythmic patterns, such as those of central pattern generator circuits (CPGs). Additionally, we propose a mechanism for transitioning between patterns. Specifically, we construct a network that can step through a sequence of five different quadruped gaits. It is composed of two dynamically distinct modules: a "counter" network that can count the number of external inputs it receives via a sequence of fixed points and a locomotion network that encodes five different quadruped gaits as limit cycles. A sequence of locomotive gaits is obtained by connecting the counter network with the locomotion network. Specifically, we introduce a new architecture for layering networks that produces fusion attractors, binding pairs of attractors from individual layers. All of this is accomplished within a unified framework of attractor-based models using threshold-linear networks.