Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation

G. Bard Ermentrout (), Stefanos E. Folias () and Zachary P. Kilpatrick ()
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G. Bard Ermentrout: University of Pittsburgh, Department of Mathematics
Stefanos E. Folias: University of Alaska Anchorage, Department of Mathematics & Statistics
Zachary P. Kilpatrick: University of Houston, Department of Mathematics

Chapter Chapter 4 in Neural Fields, 2014, pp 119-151 from Springer

Abstract: Abstract We study spatiotemporal patterns of activity that emerge in neural fields in the presence of linear adaptation Adaptation . Using an amplitude equation approach, we show that bifurcations from the homogeneous rest state can lead to a wide variety of stationary and propagating patterns on one- and two-dimensional periodic domains, particularly in the case of lateral-inhibitory synaptic weights. Other typical solutions are stationary and traveling localized activity bumps Bumps ; however, we observe exotic time-periodic localized patterns as well. Using linear stability analysis that perturbs about stationary and traveling bump Bumps solutions, we study conditions for the activity to lock to a stationary or traveling external input on both periodic and infinite one-dimensional spatial domains. Hopf and saddle-node bifurcations can signify the boundary beyond which stationary or traveling bumps Bumps Bumps traveling fail to lock to external inputs. Just beyond a Hopf bifurcation Bifurcation Hopf point, activity bumps often begin to oscillate, becoming breather Breathers or slosher Sloshers solutions.

Keywords: Hopf Bifurcation; Evans Function; Spiral Wave; Amplitude Equation; Neural Field (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-54593-1_4

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DOI: 10.1007/978-3-642-54593-1_4

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