Limit cycles in a model of olfactory sensory neurons.(English)Zbl 1414.34041
Summary: 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.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 92C30 | Physiology (general) |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C45 | Invariant manifolds for ordinary differential equations |
Cite
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