Email this article VOLTERRA OPERATOR INCLUSIONS IN THE THEORY OF GENERALIZED NEURAL FIELD MODELS WITH CONTROL. II
- Authors: Burlakov E.O.1
-
Affiliations:
- Norwegian University of Life Sciences
- Issue: Vol 22, No 1 (2017)
- Pages: 7-12
- Section: Articles
- URL: https://journal-vniispk.ru/2686-9667/article/view/362733
- DOI: https://doi.org/10.20310/1810-0198-2017-22-1-7-12
- ID: 362733
Cite item
Full Text
Abstract
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.
About the authors
Evgenii Olegovich Burlakov
Norwegian University of Life Sciences
Email: eb_@bk.ru
postgraduate As, Norway
References
Burlakov E.O. Volterra operator inclusions in the theory of generalized neural field models with control. I. // Вестник Тамбовского университета. Серия Естественные и технические науки. Тамбов, 2016. Т. 21. Вып. 6. С. 1950-1958. doi: 10.20310/1810-0198-2016-21-6-1950-1958 Burlakov E., Zhukovskiy E., Ponosov A., Wyller J. On wellposedness of generalized neural field equations with delay, // Journal of Abstract Differential Equations and Applications 2015. V. 6. P. 51-80. Burlakov E., Zhukovskiy E.S. Existence, uniqueness and continuous dependence on control of solutions to generalized neural field equations // Вестник Тамбовского университета. Серия Естественные и технические науки. Тамбов, 2015. Т. 20. Вып. 1. C. 9-16. Taube J.S., Bassett J.P. Persistent neural activity in head direction cells // Cereb. Cortex. 2003. V. 13. P. 1162-1172. Wang X-J. Synaptic reverberation underlying mnemonic persistent activity // Trends Neurosci. 2001. V. 24. P. 455-463. Tass P.A. A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations // Biological cybernetics. 2003. V. 89. P. 81-88. Suffczynski P., Kalitzin S., and Lopes Da Silva F.H. Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network // Neuroscience. 2004. V. 126. P. 467-484. Kramer M.A., Lopour B.A., Kirsch H.E., and Szeri A.J. Bifurcation control of a seizing human cortex // Physical Review E. 2006. V. 73. № 4. P. 1-16. Schiff S.J. Towards model-based control of Parkin- son’s disease // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2010. V. 368. P. 2269-2308. 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. Borisovich Yu.G., Gelman B.D., Myshkis A.D., Obukhovskii V.V. Introduction to the Theory of Multivalued Maps and Differential Inclusions. 2nd ed. Moscow: Librokom, 2011.
Supplementary files
