### Electronic Research Archive

2021, Issue 5: 3205-3226. doi: 10.3934/era.2021034
Special Issues

# Firing patterns and bifurcation analysis of neurons under electromagnetic induction

• Received: 01 November 2020 Revised: 01 March 2021 Published: 15 April 2021
• Primary: 37N25, 34C23; Secondary: 37N30, 92C20

• Based on the three-dimensional endocrine neuron model, a four-dimensional endocrine neuron model was constructed by introducing the magnetic flux variable and induced current according to the law of electromagnetic induction. Firstly, the codimension-one bifurcation and Interspike Intervals (ISIs) analysis were applied to study the bifurcation structure with respect to external stimuli and parameter $k_0$, and two dynamical behaviors were found: period-adding and period-doubling bifurcation leading to chaos. Besides, Hopf bifurcation was specially discussed corresponding to the transformation of the state. Secondly, the different firing patterns such as regular bursting, subthreshold oscillations, fast spiking, mixed-mode oscillations (MMOs) etc. can be observed by changing the external stimuli and the induced current. The neuron model presented more firing activities under strong coupling strength. Finally, the codimension-two bifurcation analysis shown more details of bifurcation. At the same time, the Bogdanov-Takens bifurcation point was also analyzed and three bifurcation curves were derived.

Citation: Qixiang Wen, Shenquan Liu, Bo Lu. Firing patterns and bifurcation analysis of neurons under electromagnetic induction[J]. Electronic Research Archive, 2021, 29(5): 3205-3226. doi: 10.3934/era.2021034

### Related Papers:

• Based on the three-dimensional endocrine neuron model, a four-dimensional endocrine neuron model was constructed by introducing the magnetic flux variable and induced current according to the law of electromagnetic induction. Firstly, the codimension-one bifurcation and Interspike Intervals (ISIs) analysis were applied to study the bifurcation structure with respect to external stimuli and parameter $k_0$, and two dynamical behaviors were found: period-adding and period-doubling bifurcation leading to chaos. Besides, Hopf bifurcation was specially discussed corresponding to the transformation of the state. Secondly, the different firing patterns such as regular bursting, subthreshold oscillations, fast spiking, mixed-mode oscillations (MMOs) etc. can be observed by changing the external stimuli and the induced current. The neuron model presented more firing activities under strong coupling strength. Finally, the codimension-two bifurcation analysis shown more details of bifurcation. At the same time, the Bogdanov-Takens bifurcation point was also analyzed and three bifurcation curves were derived.

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