Two-point heterogeneous connections in a continuum neural field model
Brackley, C. A. and Turner, Matthew S.. (2009) Two-point heterogeneous connections in a continuum neural field model. Biological Cybernetics, Vol.100 (No.5). pp. 371-383. ISSN 0340-1200Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s00422-009-0308-7
We examine a novel heterogeneous connection scheme in a 1D continuum neural field model. Multiple two-point connections are added to a local connection function in order to model the "patchy" connections seen in, for example visual cortex. We use a numerical approach to solve the equations, choosing the locations of the two-point connections stochastically. We observe self-sustained persistent fluctuations of activity which can be classified into two types (one of which is similar to that seen in network models of discrete excitable neurons, the other being particular to this model). We study the effect of parameters such as system size and the range, number and strength of connections, on the probability that a particular realisation of the connections is able to exhibit persistent fluctuations.
|Item Type:||Journal Article|
|Subjects:||Q Science > QC Physics
Q Science > QP Physiology
R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry
|Divisions:||Faculty of Science > Physics|
|Library of Congress Subject Headings (LCSH):||Neural networks (Neurobiology) -- Mathematical models, Computational neuroscience|
|Journal or Publication Title:||Biological Cybernetics|
|Number of Pages:||13|
|Page Range:||pp. 371-383|
|Access rights to Published version:||Restricted or Subscription Access|
|References:||Amari SI (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybern 27:77–87 Bao W, Wu JY (2003) Propagating wave and irregular dynamics: Spatiotemporal patterns of cholinergic theta oscillations in neocortex in vitro. J Neurophys 90:333–341 Brackley CA, Turner MS (2007) Random fluctuations of the firing rate function in a continuum neural field model. Phys Rev E 75:041,913 Brackley CA, Turner MS (2009) Persistent fluctuations of activity in undriven continuum neural field models with power-law connections. Phys Rev E 79:011918 Bressloff PC (1996) New mechanism for neural pattern formation. Phys Rev Lett 76(24):4644–4647 Bressloff PC (2001) Traveling fronts and wave propagation failure in an inhomogeneous neural network. Phys D Nonlinear Phenom 155(1–2):83–100 Bressloff PC (2003) Spatially periodic modulation of cortical patterns by long-range horizontal connections. Phys D Nonlinear Phenom 185(3–4):131–157 Bressloff PC, Folias SE, Prat A, Li YX (2003) Oscillatory waves in inhomogeneous neural media. Phys Rev Lett 91(17):178,101 Brunel N (2000) Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 8:183–208 Buzás P, Eysel UT, Adorján P, Kisvárday ZF (2001) Axonal topography of cortical basket cells in relation to orientation, dierection, and ocular dominance maps. J Comp Neurol 437:259–285 Coombes S (2005) Waves, bumps, and patterns in neural field theories. Biol Cybern 93:91–108 Coombes S, Owen MR (2005) Bumps, breathers, and waves in a neural network with spike frequency adaption. Phys Rev Lett 94: 148,102 Coombes S, Lord GJ, Owen MR (2003) Waves and bumps in neuronal networks with axo-dendritic synaptic interactions. Phys D Nonlinear Phenom 178:219–241 Cossart R, Aronov D, Yuste R (2003) Attractor dynamics of network up states in the neocortex. Nature 423:283–288 Ermentrout GB, Cowan JD (1979) A mathematical theory of visual hallucination patterns. Biol Cybern 34:137–150 Ermentrout GB, McLeod JB (1993) Existence and uniqueness of travelling waves for a neural network. Proc Sect A Math R Soc Edinb 123:461–478 Frigo M, Johnson SG (2005) The design and implementation of fftw3. Proc IEEE 93:216–231 Hellwig B (2000) A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex. Biol Cybern 82:111–121 Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 79(8):2554–2558 Hutt A, Atay FM (2005) Analysis of nonlocal neural fields for both general and gamma-distributed connectivities. Phys D Nonlinear Phenom 203:30–54 Hutt A, Wennekers T, Bestehorn M (2003) Pattern formation in intracortical neuronal fields. Netw Comput Neural Syst 14:351–368 Jirsa VK (2004) Connectivity and dynamics of neural information processing. Neuroinformatics 2:183–204 Jirsa VK, Kelso JAS (2000) Spatiotemporal pattern formation in neural systems with heterogeneous connection topologies. Phys Rev E 62(6):8462–8465 Malach R, Tootell RBH, Malonek D (1994) Relationship bewteen orientation domains, cytochrome oxidase stripes, and intrinsic horizontal connections in squirrel monkey area v2. Cereb Cortex 4(2):151–165 McCormick DA, Connors BW, Lighthall JW, Prince DA (1985) Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. J Neurophysiol 54(4):782–806 Nunez PL, Srinivason R (2006) Electric fields of the Brain—the neurophysics of EEG, 2nd edn. Oxford University Press, Oxford Pinto DJ, Ermentrout GB (2001) Spatially structured activity in synaptically coupled neuronal networks: I. travelling fronts and pulses. SIAM J Appl Math 62:206–225 Press H, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in fortran, 2nd edn. Cambridge University Press, Cambridge Qubbaj MR, Jirsa VK (2007) Neural field dynamics with heterogeneous connection topology. Phys Rev Lett 98(23):238,102 Robinson PA, Rennie CJ, Rowe DL (2002) Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys Rev E 65(4):041,924 Roxin A, Riecke H, Solla SA (2004) Self-sustained activity in a small-world network of excitable neurons. Phys Rev Lett 92: 198,101 Segev R, Benveniste M, Hulata E, Cohen N, Palevski A, Kapon E, Shapira Y, Ben-Jacob E (2002) Long term behavior of lithographically prepared in vitro neuronal networks. Phys Rev Lett 88:118,102 Sobol’ IM (1967) The distribution of points in a cube and the accurate evaluation of integrals. USSR Comput Math Math Phys 7(4):86– 112 Venkov N, Coombes S, Matthews P (2007) Dynamic instabilities in scalar neural field equations with space-dependent delays. Phys D Nonlinear Phenom 232:1–15 Wang XJ (2001) Synaptic reverberation underlying mnemonic persistent activity. TRENDS Neurosci 24:455–463 Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12:1–23 Wu JY, Guan L, Tsau Y (1999) Propagating activation during oscillations and evoked responses in neocortical slices. J Neurosci 19:5005–5015|
Actions (login required)