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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Modelling of Synaptic STDP and Analysis in a Two-Neuron Model

Discontinuity, Nonlinearity, and Complexity 1(2) (2012) 147--159 | DOI:10.5890/DNC.2012.04.002

V. K. Menz$^{1}$; S. Popovych$^{2}$; T.Küpper$^{3}$

$^{1}$ German Primate Center, Research Group Primate Neurobiology, Göttingen, Germany

$^{2}$ University of Cologne, Zoological Institute, Cologne, Germany

$^{3}$ University of Cologne, Mathematical Institute, Cologne, Germany

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A mathematical model is developed to describe the behaviour of spiking neurons and adaptation of synaptic weights in the framework of spike-timing-dependent plasticity (STDP) by modifying the model of STDP suggested by Gorchetchnikov, Versace, and Hasselmo [1]. As a result an STDP curve similar to that found experimentally by Bi and Poo [2] is produced. This approach is applied to a system of two integrate-and-fire neurons interacting via adapting synapses and stimulated by a constant external current. The dynamics of the considered system over long time periods is examined for both permanent and short initial stimulations. The obtained results are then compared with real data for in vivo and in vitro neurons.


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