Geodesic
Volterra operator inclusions in the theory of generalized neural field models with control. II
Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 1, pp. 7-12 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtained conditions for solvability of Volterra operator inclusions and continuous dependence of the solutions on a parameter. These results were implemented to investigation of generalized neural field equations involving control.
Keywords: Volterra operator inclusions, neural field equations, control, continuous dependence on parameters.
Mots-clés : existence of solutions 
@article{VTAMU_2017_22_1_a0,
     author = {E. O. Burlakov},
     title = {Volterra operator inclusions in the theory of generalized neural field models with {control.~II}},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {7--12},
     year = {2017},
     volume = {22},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2017_22_1_a0/}
}
TY  - JOUR
AU  - E. O. Burlakov
TI  - Volterra operator inclusions in the theory of generalized neural field models with control. II
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2017
SP  - 7
EP  - 12
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2017_22_1_a0/
LA  - en
ID  - VTAMU_2017_22_1_a0
ER  - 
%0 Journal Article
%A E. O. Burlakov
%T Volterra operator inclusions in the theory of generalized neural field models with control. II
%J Vestnik rossijskih universitetov. Matematika
%D 2017
%P 7-12
%V 22
%N 1
%U http://geodesic.mathdoc.fr/item/VTAMU_2017_22_1_a0/
%G en
%F VTAMU_2017_22_1_a0
E. O. Burlakov. Volterra operator inclusions in the theory of generalized neural field models with control. II. Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 1, pp. 7-12. http://geodesic.mathdoc.fr/item/VTAMU_2017_22_1_a0/

[1] E. O. Burlakov, “Volterra operator inclusions in the theory of generalized neural field models with control”, I, Tambov University Reports. Series: Natural and Technical Sciences, 21:6 (2016), 1950–1958 | DOI

[2] E. Burlakov, E. Zhukovskiy, A. Ponosov, J. Wyller, “On wellposedness of generalized neural field equations with delay”, Journal of Abstract Differential Equations and Applications, 6 (2015), 51–80 | MR | Zbl

[3] E. Burlakov, E. S. Zhukovskiy, “Existence, uniqueness and continuous dependence on control of solutions to generalized neural field equations”, Tambov University Reports. Series: Natural and Technical Sciences, 20:1 (2015), 9–16 | MR

[4] J. S. Taube, J. P. Bassett, “Persistent neural activity in head direction cells”, Cereb. Cortex, 13 (2003), 1162–1172 | DOI

[5] X-J. Wang, “Synaptic reverberation underlying mnemonic persistent activity”, Trends Neurosci, 24 (2001), 455–463 | DOI

[6] P. A. Tass, “A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations”, Biological cybernetics, 89 (2003), 81–88 | DOI | Zbl

[7] P. Suffczynski, S. Kalitzin, F. H. Lopes Da Silva, “Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network”, Neuroscience, 126 (2004), 467–484 | DOI

[8] M. A. Kramer, B. A. Lopour, H. E. Kirsch, A. J. Szeri, “Bifurcation control of a seizing human cortex”, Physical Review E, 73:4 (2006), 1–16 | DOI | MR

[9] Schiff S. J., “Towards model-based control of Parkin - son’s disease”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368 (2010), 2269–2308 | DOI | MR | Zbl

[10] Ruths J., Taylor P., Dauwels J., “Optimal Control of an Epileptic Neural Population Model”, Proceedings of the International Federation of Automatic Control (Cape Town, 2014)

[11] Borisovich Yu. G., Gelman B. D., Myshkis A. D., Obukhovskii V. V., Introduction to the Theory of Multivalued Maps and Differential Inclusions, 2nd ed., Librokom, Moscow, 2011 | MR