Jump-diffusion processes as models for neuronal activity

Bio Systems
Maria Teresa Giraudo, Laura Sacerdote

Abstract

Aiming at an improvement of the existing neuronal models, we consider a mixed process ensuing from the superposition of continuous diffusions and of Poisson time-distributed sequence of impulses and focus our attention on the moments of the firing time. In particular, we consider three different instances: the large jumps model in which each jump causes the neuron firing, the reset model characterized by jumps towards the resting potential and a more general model where constant amplitude excitatory and inhibitory jumps are superimposed on diffusion. By resorting to analytical arguments and to numerical computations, the main behavioral differences of the considered models are outlined.

References

Jan 1, 1991·Bio Systems·M Musila, P Lánský
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Oct 1, 1995·Biological cybernetics·P LánskýF Tomassetti
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Citations

Apr 12, 2011·Journal of Computational Neuroscience·Patrick JahnSusanne Ditlevsen
Dec 3, 2002·Bio Systems·Maria Teresa GiraudoRoberta Sirovich
Nov 20, 2013·Mathematical Biosciences and Engineering : MBE·Virginia Giorno, Serena Spina
Dec 5, 2008·IEEE Transactions on Neural Networks·Ashok Patel, Bart Kosko
Oct 21, 2016·Scientific Reports·Mehrnaz AnvariKlaus Lehnertz
Jan 23, 2020·Physical Review. E·Leonardo Rydin GorjãoM Reza Rahimi Tabar
May 10, 2017·Scientific Reports·Simona OlmiAlessandro Torcini

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