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Numerical Approximation for Nonlinear Noisy Leaky Integrate-and-Fire Neuronal Model

Author

Listed:
  • Dipty Sharma

    (School of Mathematics, Thapar Institute of Engineering & Technology, Patiala 147004, India)

  • Paramjeet Singh

    (School of Mathematics, Thapar Institute of Engineering & Technology, Patiala 147004, India)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A& M University-Kingsville, Kingsville, TX 78363, USA)

  • Mehmet Emir Koksal

    (Department of Mathematics, Ondokuz Mayis University, Atakum, Samsun 55139, Turkey)

Abstract

We consider a noisy leaky integrate-and-fire (NLIF) neuron model. The resulting nonlinear time-dependent partial differential equation (PDE) is a Fokker-Planck Equation (FPE) which describes the evolution of the probability density. The finite element method (FEM) has been proposed to solve the governing PDE. In the realistic neural network, the irregular space is always determined. Thus, FEM can be used to tackle those situations whereas other numerical schemes are restricted to the problems with only a finite regular space. The stability of the proposed scheme is also discussed. A comparison with the existing Weighted Essentially Non-Oscillatory (WENO) finite difference approximation is also provided. The numerical results reveal that FEM may be a better scheme for the solution of such types of model problems. The numerical scheme also reduces computational time in comparison with time required by other schemes.

Suggested Citation

  • Dipty Sharma & Paramjeet Singh & Ravi P. Agarwal & Mehmet Emir Koksal, 2019. "Numerical Approximation for Nonlinear Noisy Leaky Integrate-and-Fire Neuronal Model," Mathematics, MDPI, vol. 7(4), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:363-:d:224738
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    Cited by:

    1. Ghinwa El Masri & Asma Ali & Waad H. Abuwatfa & Maruf Mortula & Ghaleb A. Husseini, 2023. "A Comparative Analysis of Numerical Methods for Solving the Leaky Integrate and Fire Neuron Model," Mathematics, MDPI, vol. 11(3), pages 1-15, January.

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