Generalized Hopf bifurcation emanated from a corner for piecewise smooth planar systems

2005 ◽  
Vol 62 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Yongkui Zou ◽  
Tassilo Küpper
Keyword(s):  
Hopf Bifurcation ◽  
Piecewise Smooth ◽  
Generalized Hopf Bifurcation ◽  
Planar Systems

Normal form for generalized Hopf bifurcation with non-semisimple 1 ? 1 resonance

1994 ◽  
Vol 45 (2) ◽  
pp. 312-335 ◽  
Author(s):  
N. Sri Namachchivaya ◽  
Monica M. Doyle ◽  
William F. Langford ◽  
Nolan W. Evans
Keyword(s):  
Hopf Bifurcation ◽  
Normal Form ◽  
Generalized Hopf Bifurcation

scholarly journals Limit Cycles in a Model of Olfactory Sensory Neurons

2019 ◽  
Vol 29 (03) ◽  
pp. 1950038 ◽  
Author(s):  
Yonghui Xia ◽  
Mateja Grašič ◽  
Wentao Huang ◽  
Valery G. Romanovski
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycle ◽  
Sensory Neurons ◽  
Limit Cycles ◽  
Center Manifold ◽  
Calcium Oscillations ◽  
Olfactory Sensory Neurons ◽  
Generalized Hopf Bifurcation ◽  
Subcritical Hopf Bifurcation ◽  
Unstable Cycle

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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