Struggling tadpoles and Big Bang Bifurcations
Fluids and Materials Seminar
8th February 2018, 2:00 pm – 3:00 pm
Main Maths Building, SM3
Xenopus hatchling tadpoles "struggle" when held at their tail, rhythmically bending their body in an attempt to free themselves. During struggling, neurons on opposite sides of the tadpole spinal cord fire bursts of spikes in alternation, resulting in motor activity and the rhythmic bends of the whole body. In this talk I will present a reduced tadpole struggling model that consists of two spiking neurons mutually coupled through synaptic inhibition with short-term depression, where each neuron represents one side of the spinal cord. This two-cell network can produce stable periodic anti-phase burst patterns resembling the struggling rhythm seen in tadpoles. Methods of geometric singular perturbation theory will be employed to reduce the network to a partially continuous, scalar Poincare map. We will demonstrate that the multidimensional parameter space of the full two-cell model is structured by a pair of Big Bang Bifurcations of that scalar map.