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Limit Cycles in a Model of Olfactory Sensory Neurons

Yonghui Xia

Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China

E-mail Address: xiadoc@163.com

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Mateja Grašič

Faculty of Natural Science and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia

Institute of Mathematics, Physics and Mechanics, SI-1000 Ljubljana, Slovenia

E-mail Address: mateja.grasic@um.si

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Wentao Huang

http://orcid.org/0000-0002-6420-3232

School of Science, Guilin University of Aerospace Technology, Guilin 541004, P. R. China

E-mail Address: huangwentao@163.com

Corresponding author

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, and

Valery G. Romanovski

Faculty of Natural Science and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia

Faculty of Electrical Engineering and Computer Science, University of Maribor, SI-2000 Maribor, Slovenia

Center for Applied Mathematics and Theoretical Physics, SI-2000 Maribor, Slovenia

E-mail Address: valery.romanovsky@uni-mb.si

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https://doi.org/10.1142/S021812741950038XCited by:12 (Source: Crossref)

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.

Keywords:

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