caa a22 4500 46324494X CHVBK 20180405153323.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s00422-007-0167-z doi (NATIONALLICENCE)springer-10.1007/s00422-007-0167-z Neural network firing-rate models on integral form [Elektronische Daten] Effects of temporal coupling kernels on equilibrium-state stability [Øyvind Nordbø, John Wyller, Gaute Einevoll] Firing-rate models describing neural-network activity can be formulated in terms of differential equations for the synaptic drive from neurons. Such models are typically derived from more general models based on Volterra integral equations assuming exponentially decaying temporal coupling kernels describing the coupling of pre- and postsynaptic activities. Here we study models with other choices of temporal coupling kernels. In particular, we investigate the stability properties of constant solutions of two-population Volterra models by studying the equilibrium solutions of the corresponding autonomous dynamical systems, derived using the linear chain trick, by means of the Routh-Hurwitz criterion. In the four investigated synaptic-drive models with identical equilibrium points we find that the choice of temporal coupling kernels significantly affects the equilibrium-point stability properties. A model with an α-function replacing the standard exponentially decaying function in the inhibitory coupling kernel is in most of our examples found to be most prone to instability, while the opposite situation with an α-function describing the excitatory kernel is found to be least prone to instability. The standard model with exponentially decaying coupling kernels is typically found to be an intermediate case. We further find that stability is promoted by increasing the weight of self-inhibition or shortening the time constant of the inhibition. Springer-Verlag, 2007 Neural networks nationallicence Firing rate nationallicence Volterra nationallicence Stability nationallicence Temporal coupling nationallicence Routh-Hurwitz nationallicence Nordbø Øyvind Department of Mathematical Sciences and Technology and Center for Integrative Genetics, Norwegian University of Life Sciences, P. O. Box 5003, 1432, Ås, Norway aut Wyller John Department of Mathematical Sciences and Technology and Center for Integrative Genetics, Norwegian University of Life Sciences, P. O. Box 5003, 1432, Ås, Norway aut Einevoll Gaute Department of Mathematical Sciences and Technology and Center for Integrative Genetics, Norwegian University of Life Sciences, P. O. Box 5003, 1432, Ås, Norway aut Biological Cybernetics Springer-Verlag 97/3(2007-09-01), 195-209 0340-1200 97:3<195 2007 97 422 https://doi.org/10.1007/s00422-007-0167-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00422-007-0167-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nordbø Øyvind Department of Mathematical Sciences and Technology and Center for Integrative Genetics, Norwegian University of Life Sciences, P. O. Box 5003, 1432, Ås, Norway aut NATIONALLICENCE 700 1- Wyller John Department of Mathematical Sciences and Technology and Center for Integrative Genetics, Norwegian University of Life Sciences, P. O. Box 5003, 1432, Ås, Norway aut NATIONALLICENCE 700 1- Einevoll Gaute Department of Mathematical Sciences and Technology and Center for Integrative Genetics, Norwegian University of Life Sciences, P. O. Box 5003, 1432, Ås, Norway aut NATIONALLICENCE 773 0- Biological Cybernetics Springer-Verlag 97/3(2007-09-01), 195-209 0340-1200 97:3<195 2007 97 422 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer