Classification of Rhythmic Patterns in the

Abstract--There is a large class of central pattern generators that may change their rhythmic output under the influence of neuromodulators. The generation of patterns by neural etworks is dependent on mechanisms that operate on different time scales. We present a classification scheme for the rhythmic patterns that may be generated by small neural networks, as a method for investigating the biological mechanisms responsible for pattern generation and pattern switching. Discrete methods based on transition graphs are applied to dynamic biological networks to map out the set of possible rhythmic behaviors. There is a restriction in the number of patterns that may ari e due to specific mechanisms and it is possible to identify the routes that are available for switching between different patterns. A measure is introduced onto the set of rhythms to quantify their differences and organize the set according to clusters of similar rhythms. Each cluster represents a different operational mode of the network. Examples are drawn from the stomatogastric ganglion, a well studied network that controls the musclesof the foregut in crustaceans. Classes of rhythms are found that correspond to experimentally observed patterns. In addition, other classes of rhythms are found that have not yet been observed. Th method presented here proves to be anefficient means to scan the space of possible rhythms that can be generated by a small neural network