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Laing, Carlo; Coombes, Stephen (2005)
Languages: English
Types: Article
Subjects:
In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques we construct the Evans function characterising the stability of both stationary and travelling wave solutions, under the assumption that the firing rate function is the Heaviside step. We find that these differences in timing for the two populations can cause instabilities of these solutions, leading to, for example, stationary breathers. We also analyse $quot;anti-pulses,$quot; a novel type of pattern for which all but a small interval of the domain (in moving coordinates) is active. These results extend previous work on neural fields with space dependent delays, and demonstrate the importance of considering the effects of the different time-courses of excitatory and inhibitory neural activity.
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    • [1] P Blomquist, J Wyller, and G T Einevoll. Localized activity patterns in two-population neuronal networks. Physica D, 206:180-212, 2005.
    • [2] P C Bressloff. Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons. Journal of Mathematical Biology, 40:169-198, 2000.
    • [3] P C Bressloff and S E Folias. Front-bifurcations in an excitatory neural network. SIAM Journal on Applied Mathematics, 65:131-151, 2004.
    • [4] P C Bressloff, S E Folias, A Prat, and Y X Li. Oscillatory waves in inhomogeneous neural media. Physical Review Letters, 91:178101, 2003.
    • [6] S Coombes, G J Lord, and M R Owen. Waves and bumps in neuronal networks with axo-dendritic synaptic interactions. Physica D, 178:219-241, 2003.
    • [20] X Huang, W C Troy, Q Yang, H Ma, C R Laing, S J Schiff, and J Wu. Spiral waves in disinhibited mammalian neocortex. The Journal of Neuroscience, 24:9897-9902, 2004.
    • [22] A Hutt, M Bestehorn, and T Wennekers. Pattern formation in intracortical neuronal fields. Network: Computation in Neural Systems, 14:351-368, 2003.
    • [34] D J Pinto, R K Jackson, and C E Wayne. Existence and stability of traveling pulses in a continuous neuronal network. SIAM Journal on Applied Dynamical Systems, 4:954-984, 2005.
    • [35] A Roxin, N Brunel, and D Hansel. Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks. Physical Review Letters, 94:238103, 2005.
    • [36] L P Shayer and S A Campbell. Stability, bifurcation, and multistability in a system of two coupled neurons with multiple time delays. SIAM Journal on Applied Mathematics, 61:673-700, 2000.
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