Bifurcations of Limit Cycles in a Reduced Model of the Xenopus Tadpole Central Pattern Generator

Journal of Mathematical Neuroscience
Andrea FerrarioRoman Borisyuk

Abstract

We present the study of a minimal microcircuit controlling locomotion in two-day-old Xenopus tadpoles. During swimming, neurons in the spinal central pattern generator (CPG) generate anti-phase oscillations between left and right half-centres. Experimental recordings show that the same CPG neurons can also generate transient bouts of long-lasting in-phase oscillations between left-right centres. These synchronous episodes are rarely recorded and have no identified behavioural purpose. However, metamorphosing tadpoles require both anti-phase and in-phase oscillations for swimming locomotion. Previous models have shown the ability to generate biologically realistic patterns of synchrony and swimming oscillations in tadpoles, but a mathematical description of how these oscillations appear is still missing. We define a simplified model that incorporates the key operating principles of tadpole locomotion. The model generates the various outputs seen in experimental recordings, including swimming and synchrony. To study the model, we perform detailed one- and two-parameter bifurcation analysis. This reveals the critical boundaries that separate different dynamical regimes and demonstrates the existence of parameter regions of bi-stab...Continue Reading

References

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Citations

Mar 23, 2019·Proceedings. Biological Sciences·Alan RobertsStephen R Soffe
Jan 9, 2019·Journal of Mathematical Neuroscience·Zachary P KilpatrickRobert Rosenbaum
May 4, 2021·Journal of Mathematical Neuroscience·Andrea Ferrario, James Rankin

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