Influence of neurobiological mechanisms on speeds of traveling wave fronts in mathematical neuroscience
Pages: 1003 - 1037, Issue 3, October 2011

doi:10.3934/dcdsb.2011.16.1003      Abstract        References        Full text (1670.2K)           Related Articles

Linghai Zhang - Department of Mathematics, Lehigh University, 14 East Packer Avenue, Bethlehem, Pennsylvania 18015, United States (email)
Ping-Shi Wu - Department of Mathematics, Lehigh University, 14 East Packer Avenue, Bethlehem, Pennsylvania 18015, United States (email)
Melissa Anne Stoner - Department of Mathematics, Lehigh University, 14 East Packer Avenue, Bethlehem, Pennsylvania 18015, United States (email)

1	Fatihcan M. Atay and Axel Hutt, Stability and bifurcations in neural fields with finite propagation speed and general connectivity, SIAM Journal on Applied Mathematics, 65 (2004), 644-666.
2	Fatihcan M. Atay and Axel Hutt, Neural fields with distributed transmission speeds and long-range feedback delays, SIAM Journal on Applied Dynamical Systems, 5 (2006), 670-698.
3	Stephen Coombes, Gabriel J. Lord and Markus R. Owen, Waves and bumps in neuronal networks with axo-dendritic synaptic interactions, Physica D, 178 (2003), 219-241.
4	Stephen Coombes and Markus R. Owen, Evans functions for integral neural field equations with Heaviside firing rate function, SIAM Journal on Applied Dynamical Systems, 3 (2004), 574-600.
5	Axel Hutt and Fatihcan M. Atay, Analysis of nonlocal neural fields for both general and gamma-distributed connectivities, Physica D, 203 (2005), 30-54.
6	Axel Hutt and Fatihcan M. Atay, Effects of distributed transmission speeds on propagating activity in neural populations, Physical Review E, Statistical, nonlinear, and soft matter physics, 73 (2006), 021906.
7	Felicia Maria G. Magpantay and Xingfu Zou, Wave fronts in neuronal fields with nonlocal post-synaptic axonal connections and delayed nonlocal feedback connections, Mathematical Biosciences and Engineering, 7 (2010), 421-442.
8	David J. Pinto and G. Bard Ermentrout, Spatially structured activity in synaptically coupled neuronal networks. I. traveling fronts and pulses, II. Lateral inhibition and standing pulses, SIAM Journal on Applied Mathematics, 62 (2001), I. 206-225, II. 226-243.
9	Hugh R. Wilson and Jack D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons, Biophysical Journal, 12 (1972), 1-24.
10	Hugh R. Wilson and Jack D. Cowan, A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue, Kybernetic, 13 (1973), 55-80.
11	Eiji Yanagida and Linghai Zhang, Speeds of traveling waves of some integral differential equations, Japan Journal of Industrial and Applied Mathematics, 27 (2010), 347-373.
12	Linghai Zhang, Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks, Journal of Differential Equations, 197 (2004), 162-196.
13	Linghai Zhang, Traveling waves of a singularly perturbed system of integral-differential equations arising from neuronal networks, Journal of Dynamics and Differential Equations, 17 (2005), 489-522.
14	Linghai Zhang, How do synaptic coupling and spatial temporal delay influence traveling waves in nonlinear nonlocal neuronal networks?, SIAM Journal on Applied Dynamical Systems, 6 (2007), 597-644.
15	Linghai Zhang, Traveling Waves Arising from Synaptically Coupled Neuronal Networks, Advances in Mathematics Research. Editor-in-Chief: Albert R. Baswell. Nova Science Publishers Inc. New York. ISBN: 978-1-60876-265-1. 10 (2010), 53-204.
16	Linghai Zhang, Ping-Shi Wu and Melissa Anne Stoner, Influence of sodium currents on speeds of traveling wave fronts in synaptically coupled neuronal networks, Physica D, 239 (2010), 9-32.

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