Limit Cycles in a Model of Olfactory Sensory Neurons
Y. Xia, M. Gra\v{s}i\v{c}, W. Huang, V. Romanovski
TL;DR
This paper introduces a method for analyzing small limit cycle bifurcations in parameter-dependent systems and applies it to a model of calcium oscillations in olfactory neurons, revealing the existence of multiple limit cycles.
Contribution
It develops an approach to study bifurcations on a center manifold and applies it to a biological neuron model, uncovering complex oscillatory behaviors.
Findings
The model exhibits two limit cycles: a stable one after a Bautin bifurcation.
An unstable limit cycle appears following a subcritical Hopf bifurcation.
The method effectively analyzes bifurcations in biological oscillatory systems.
Abstract
We propose an approach to study small limit cycle bifurcations on a center manifold in analytic or smooth systems depending on parameters. We then apply it to the investigation of limit cycle bifurcations in a model of calcium oscillations in the cilia of olfactory sensory neurons and show that it can have two limit cycles: a stable cycle appearing after a Bautin (generalized Hopf) bifurcation and an unstable cycle appearing after a subcritical Hopf bifurcation.
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