Bifurcation analysis on the reduced dopamine neuronal model

Xiaofang Jiang; Hui Zhou; Feifei Wang; Bingxin Zheng; Bo Lu; Xiaofang Jiang; Hui Zhou; Feifei Wang; Bingxin Zheng; Bo Lu

doi:10.3934/era.2024191

Electronic Research Archive

2024, Volume 32, Issue 7: 4237-4254. doi: 10.3934/era.2024191

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Research article

Bifurcation analysis on the reduced dopamine neuronal model

School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang 453003, China

Received: 22 April 2024 Revised: 19 June 2024 Accepted: 28 June 2024 Published: 04 July 2024

Bursting is a crucial form of firing in neurons, laden with substantial information. Studying it can aid in understanding the neural coding to identify human behavioral characteristics conducted by these neurons. However, the high-dimensionality of many neuron models imposes a difficult challenge in studying the generative mechanisms of bursting. On account of the high complexity and nonlinearity characteristic of these models, it becomes nearly impossible to theoretically study and analyze them. Thus, this paper proposed to address these issues by focusing on the midbrain dopamine neurons, serving as the central neuron model for the investigation of the bursting mechanisms and bifurcation behaviors exhibited by the neuron. In this study, we considered the dimensionality reduction of a high-dimensional neuronal model and analyzed the dynamical properties of the reduced system. To begin, for the original thirteen-dimensional model, using the correlation between variables, we reduced its dimensionality and obtained a simplified three-dimensional system. Then, we discussed the changing characteristics of the number of spikes within a burst by simultaneously varying two parameters. Finally, we studied the co-dimension-2 bifurcation in the reduced system and presented the bifurcation behavior near the Bogdanov-Takens bifurcation.
- dopamine neurons,
- dimensionality reduction,
- firing rate,
- inter-spike interval,
- bifurcation
Citation: Xiaofang Jiang, Hui Zhou, Feifei Wang, Bingxin Zheng, Bo Lu. Bifurcation analysis on the reduced dopamine neuronal model[J]. Electronic Research Archive, 2024, 32(7): 4237-4254. doi: 10.3934/era.2024191

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Abstract

Bursting is a crucial form of firing in neurons, laden with substantial information. Studying it can aid in understanding the neural coding to identify human behavioral characteristics conducted by these neurons. However, the high-dimensionality of many neuron models imposes a difficult challenge in studying the generative mechanisms of bursting. On account of the high complexity and nonlinearity characteristic of these models, it becomes nearly impossible to theoretically study and analyze them. Thus, this paper proposed to address these issues by focusing on the midbrain dopamine neurons, serving as the central neuron model for the investigation of the bursting mechanisms and bifurcation behaviors exhibited by the neuron. In this study, we considered the dimensionality reduction of a high-dimensional neuronal model and analyzed the dynamical properties of the reduced system. To begin, for the original thirteen-dimensional model, using the correlation between variables, we reduced its dimensionality and obtained a simplified three-dimensional system. Then, we discussed the changing characteristics of the number of spikes within a burst by simultaneously varying two parameters. Finally, we studied the co-dimension-2 bifurcation in the reduced system and presented the bifurcation behavior near the Bogdanov-Takens bifurcation.

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