2003
DOI: 10.1088/0954-898x_14_2_310
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Pattern formation in intracortical neuronal fields

Abstract: This paper introduces a neuronal field model for both excitatory and inhibitory connections. A single integro-differential equation with delay is derived and studied at a critical point by stability analysis, which yields conditions for static periodic patterns and wave instabilities. It turns out that waves only occur below a certain threshold of the activity propagation velocity. An additional brief study exhibits increasing phase velocities of waves with decreasing slope subject to increasing activity propa… Show more

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Cited by 92 publications
(104 citation statements)
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“…This condition defines the critical wave number k c and does not depend on the synaptic time scales and the conduction speed in accordance with previous studies on populations Cogn Neurodyn (2010) 4:37-59 47 of a single neuron type (Hutt et al 2003;Atay and Hutt 2005;Venkov et al 2007). Considering the loss of stability to the spatially homogeneous state (k = 0) the threshold condition reads 1 = d E (p)a e -f(p)d I (p)a i which coincides with the condition (20) for the points A and B, cf.…”
Section: The Resting Statesupporting
confidence: 88%
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“…This condition defines the critical wave number k c and does not depend on the synaptic time scales and the conduction speed in accordance with previous studies on populations Cogn Neurodyn (2010) 4:37-59 47 of a single neuron type (Hutt et al 2003;Atay and Hutt 2005;Venkov et al 2007). Considering the loss of stability to the spatially homogeneous state (k = 0) the threshold condition reads 1 = d E (p)a e -f(p)d I (p)a i which coincides with the condition (20) for the points A and B, cf.…”
Section: The Resting Statesupporting
confidence: 88%
“…The model (11) extends previous standard neural field models for a single neural population Hutt et al 2003;Amari 1977;Coombes et al 2003) by an additional population. We observe that the right hand sides of Eqs.…”
Section: Methodsmentioning
confidence: 70%
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“…Analogous systems have been shown to support a number of spatiotemporal solutions like patterns reminiscent of hallucinations [16,17], traveling fronts [18][19][20], traveling pulses [21], and stationary pulses [22]. One additional detail to consider is the effects of finite axonal conduction velocities by including delay terms in the evolution equations [21,23,24]. Also, negative feedback processes like synaptic depression and spike frequency adaptation have been introduced in some neural field models as auxiliary variables [12,21,25,26].…”
Section: Introductionmentioning
confidence: 99%