Stability and bifurcation of the Tsodyks-Markram model about short-term synaptic plasticity with time delay
Department of mathematics and physics, Shijiazhuang Tiedao University, 050043, Shijiazhuang, P.R. China
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Revised: 13 April 2014
Accepted: 18 April 2014
Published online: 2 June 2014
Short-term synaptic plasticity in the Tsodyks-Markram model can lead to unpredictable and complicated network dynamics. In this paper, we present a new Tsodyks-Markram model with time delay as a parameter. The time delay plays a very important role for the dynamics of our model. We report on the existence of Hopf bifurcation in the model for fixed and varied release probability of available neurotransmitters. It is found that there are stability switches, and a supercritical or subcritical Hopf bifurcation occur when the delay passes through a sequence of critical values. We provide numerical results to illustrate our conclusion about stability and obtain the properties of Hopf bifurcation. Moreover, we find the large sensitivity to initial conditions in our model.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2014