High-order finite volume approximation for population density model based on quadratic integrate-and-fire neuron
ISSN: 0264-4401
Article publication date: 23 November 2018
Issue publication date: 8 February 2019
Abstract
Purpose
The purpose of this paper is to develop and apply a high-order numerical method based on finite volume approximation for quadratic integrate-and-fire (QIF) neuron model with the help of population density approach.
Design/methodology/approach
The authors apply the population density approach for the QIF neuron model to derive the governing equation. The resulting mathematical model cannot be solved with existing analytical or numerical techniques owing to the presence of delay and advance. The numerical scheme is based along the lines of approximation: spatial discretization is performed by weighted essentially non-oscillatory (WENO) finite volume approximation (FVM) and temporal discretization are performed by strong stability-preserving explicit Runge–Kutta (SSPERK) method. Compared with existing schemes of orders 2 and 3 from the literature, the proposed scheme is found to be more efficient and it produces accurate solutions with few grid cells. In addition to this, discontinuity is added in the application of the model equation to illustrate the high performance of the proposed scheme.
Findings
The developed scheme works nicely for the simulation of the resulting model equation. The authors discussed the role of inhibitory and excitatory parts in variation of neuronal firing. The validation of the designed scheme is measured by its comparison with existing schemes in the literature. The efficiency of the designed scheme is demonstrated via numerical simulations.
Practical implications
It is expected that the present study will be a useful tool to tackle the complex neuron model and related studies.
Originality/value
The novel aspect of this paper is the application of the numerical methods to study the modified version of leaky integrate-and-fire neuron based on a QIF neuron. The model of the current study is inspired from the base model given in Stein (1965) and modified version in Kadalbajoo and Sharma (2005) and Wang and Zhang (2014). The applicability was confirmed by taking some numerical examples.
Keywords
Acknowledgements
The authors would like to thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions.
Funding: The author Mr Santosh Kumar is thankful to the University Grants Commission, Government of India for providing financial assistance in terms of Senior Research Fellowship (F. 2-16/2011(SA-I)).
Citation
Singh, P., Kumar, S. and Koksal, M.E. (2019), "High-order finite volume approximation for population density model based on quadratic integrate-and-fire neuron", Engineering Computations, Vol. 36 No. 1, pp. 84-102. https://doi.org/10.1108/EC-11-2017-0445
Publisher
:Emerald Publishing Limited
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