PHASE AND EXACT MODELS FOR MULTIFUNCTIONAL CENTRAL PATTERN GENERATORS

We compare multistability in central pattern genera-tor (CPG) motifs comprised either of biologically plausible Hodgkin-Huxley models of bursting leech heart interneurons or of phenomenologically reduced phase models. We propose a novel computational tool for detailed examination of polyrhyth-mic bursting in biophysical CPG models with coupling asymme-tries and arbitrary coupling strength. We carry out the compar-ison of the 3-cell motifs with reciprocally inhibitory asymmetric connections by reducing the consideration to the examination of the qualitative geometric structure of two-dimensional maps for phase lag between the bursting cells. 3-CELL MOTIFS The ability of distinct neural anatomical circuits, such as central pattern generators (CPG), to generate multiple bursting patterns determining motor behaviors such as heartbeat, respira-tion, and locomotion is widespread in animals and humans [1,2]. While a dedicated CPG generates a single pattern robustly, a multifunctional CPG can flexibly produce distinct rhythms, such as temporarily distinct swimming versus crawling, and alterna-tion of blood circulation patterns in leeches, for example [3]. Multistability enhances the flexibility of nervous systems and has far reaching implications for motor control, dynamic memory, information processing, and decision making in humans and ani-mals. Switching between locomotive behaviors can be attributed to switching between various attractors of a CPG network [4]. Each attractor is associated with a definite rhythm on a specific time scale. The emergence of synchronous rhythms in neural net-works is closely related to temporal characteristics of the coupled ∗Address all correspondence to this author