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Our paper N A Venkov, S Coombes, P C Matthews "Dynamic instabilities in scalar neural field equations with space-dependent delays" has been published in Physica D! There is also a preprint here.

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Nikola Atanasov Venkov
born 19.XI.1981, Bulgarian. Currently in United Kingdom.
2nd year PhD student at the School of Mathematical Sciences, University of Nottingham under the supervision of Dr Stephen Coombes.
Title of project: "Dynamics of Neural field models", more specificly I study pattern formation. (see below)

Academic address:
School of Mathematical Sciences
University of Nottingham
Nottingham NG7 2RD
United Kingdom

My electronic address is nikola.venkov @ the departm.ent .uk server of maths.nottingham.ac.uk
Phone number: +44-(0)79-8594-1179
Fax number: +44-(0)115-951-4951

My CV (in pdf format) - you will also find more information on my research there.

Research statement:

       Travelling waves of localised high neuronal activity have been observed in experimental preparations of cortical and thalamic brain slices. In vivo, EEG rhythms and brain activity during epileptic seizures are striking phenomena of large-scale synchronisation of neuronal populations. Using mathematical description of neural tissue by integro-differential equations linking the intrinsic local population dynamics with the nonlocal synaptic coupling between populations one is able to achieve similar type of dynamics. I am studying pattern formation in such nonlocal neural field models by adapting techniques that have been developed in physics for local PDE equations.
       Results for more complicated neural field models have not been that common although they are both biologically more realistic and can produce more interesting dynamic patterns. We are interested in models incorporating space-dependent delays (axonal or dendritic) in the biologically relevant regime of local inhibition-distal excitation connectivity, and models involving various types of adaptation, including dynamic thresholds. The additional features allow interesting solutions even for one-population reductions of the models. We have studied globally periodic solutions by Turing-Hopf instability theory, both linear and weakly non-linear (deriving amplitude equations).
       We have undertaken this analysis for a general 1D model with any time-dependent connectivity allowing us to study models with various types of delays and adaptation. We formulated also the full PDE form and studied instabilities in a 2D multi-population model with axonal delays which is applicable to EEG simulation. Currently we are looking at approaches for understanding localised solutions in 1D and 2D fields. Solutions of models incorporating dynamic threshold have characteristics very similar to dispersive solitons found in various physical systems and we are adapting techniques from those fields to handle integral equations.

Forthcoming presentations:
I will present a poster discussing some ethical implications of progress in Theoretical Neuroscience
       in the session perspectives 2007, BA Festival of Science, York, 9 - 15.IX.2007

Past presentations:
A poster, comparison of Amari and Evans approaches, presented at
       SIAM Conference on Applications of Dynamical Systems, Snowbird, USA, 28.V - 1.VI.2007
A talk at Theoretical Neuroscience Network Annual Meeting 2006, University of Bristol, Bristol, UK, 6 - 8.IX.2006
Poster "Amplitude equations for a class of neural field models" (three page resume) at CNS 2006, Edinburgh, UK, 16 - 20.VII.2006
It will also feature on the Conference on Mathematical Neuroscience NEUROMATH 06, Universitat d'Andorra, Andora, 1 - 4.IX.2006
A talk at VI. Crimean School and Workshops: Nonlinear Dynamics, Chaos, and Applications, Yalta, Crimea, Ukraine, 15 - 26.V.2006
Poster for Coupled60: a workshop on coupled systems, Houston, USA, 3-6.II.2005
       with title "Neural Field Model with Axonal Time-Delay: Generation of Travelling Turing Patterns"
Poster displayed at Workshop on Mathematical Neuroscience, Edinburgh, United Kingdom, 21 - 23.III.2005
Also at PFD III: Theoretical Aspects of Pattern Formation, Guilford, United Kingdom, 19 - 23.IX.2005