RESEARCH OF DYNAMIC MODES IN THE MATHEMATICAL MODEL OF ELEMENTARY THALAMOCORTICAL CELL
Cite this article as:
Kolosov A. V., Nujdel I. V., Yakhno V. G. RESEARCH OF DYNAMIC MODES IN THE MATHEMATICAL MODEL OF ELEMENTARY THALAMOCORTICAL CELL. Izvestiya VUZ. Applied Nonlinear Dynamics, 2016, vol. 24, iss. 5, pp. 72-83. DOI: https://doi.org/10.18500/0869-6632-2016-24-5-72-83
In the work the mathematical model of the thalamocortical network’s unit cell and it’s characteristic dynamical modes in system, describing the interaction between a thalamus, thalamus reticular nucleus and a cortex, is studied.
During normal information processing, input signal gating occurs in time in the thalamo-cortical network. The violation of the normal functioning leads to an epilepsy, when the perception of information is disrupted. The consideration of this system will lead to an understanding of the human perception’s violation regularities, which correspond to the thalamo-cortical network’s self-oscillation.
The focused mathematical model is described by a system of three differential equations. For this system a three-dimensional phase space is constructed, enabling us to track changes of the system’s «equilibrium states» when parameters change.
The analysis of the system for the first time is performed using a three-dimensional phase space; the behavior of the representative points’ trajectories is considered, and the representation of equilibrium states of the system becomes obvious. Due to the large number of parameters of the system to build that space makes it easier to predict the development of the system in subsequent time for any parameters.
The classification of dynamical modes in system (unexcited, excited and a self-oscillation), depending on the magnitude of the constant external signal incoming to the thalamus, is carried out. It is shown that the response of the system consists of a first pulse and following it self-oscillation pulses, whose period is different from the duration of the first pulse. The dependence of characteristic times of the first impulse response and the period of the self-oscillation with the external signal is studied.
The numerical analysis of the model revealed the existence of U-shaped dependence of the first pulse duration and a decreasing of the period of the self-oscillation in the response to the increase of the external signal value. The results are important for further consideration of the plausibility of the hypothesis, according to which the thalamocortical networks control the activity of the areas of the cerebral cortex and focused (normally) on the integration of the obtained results for decision-making at higher levels of neural network processing in brain structures.
DOI: 10.18500/0869-6632-2016-24-5-72-83
Paper reference: Kolosov A.V., Nuidel I.V., Yakhno V.G. Research of dynamic modes in the mathematical model of elementary thalamocortical cell. Izvestiya VUZ. Applied Nonlinear Dynamics. 2016. Vol. 24. Issue 5. P. 72–83.
1. Hecht-Nielsen R. A theory of the cerebral cortex // Proceedings of the 6th International Conference on Molecular Electronics and Biocomputing, Future Electronic Devices Association of Japan, Okinawa, 28–30 November 1995.
2. Coulter D.A. Thalamocortical Anatomy and Physiology, Epilepsy: A Comprehensive Textbook // J. Engel (ed.), Jr. and T.A.Pedley, Liippincott Raven Publisher: Piladelphia, 1997. 341 р.
3. Haber S.N., Calzavara R. The cortico-basal ganglia integrative network: The role of the thalamus // Brain Research Bulletin. 2009. Vol. 78. P. 69–74.
4. Silkis I.G. The contribution of synaptic plasticity in the basal ganglia in the processing of visual information (hypothetical mechanism) // Journal higher nervous activity. 2006. Vol. 56. No 6 (In Russian).
5. Human Physiology / Eds V.M Pokrovsky, G.F. Korot’ko. Тextbook, 2nd ed., Rev. and ext. M.: 2003. 656 p. (In Russian).
6. Vinogradova O.S. Hippocampus and memory. M.: Nauka, 1975. (In Russian).
7. Borysiuk R. Simulation hippocampal theta rhythm// Journal of Higher Nervous Activity. 2004. Vol. 54, No 1. P. 85–100 (In Russian).
8. Shevelev I.A. Wave Processes in the Visual Cortex // J. Priroda. 2001. N12. P. 10. http://vivovoco.rsl.ru/VV/JOURNAL/NATURE/12_01/ALPHA.HTM
9. Yakhno V.G., Bellyustin N.S., Krasil’nikova I.G., Kuznetsov S.O., Nuidel I.V., Panfilov A.I., Perminov A.O., Shadrin A.V., Shevyrev A.A. The research system of decision-making by fragments of a complex image using neuron algorithms // Izvestia VUZ. Radiophysics. 1994, Vol. 37, N8. Pp. 961–986 (In Russian).
10. Yakhno V.G. Models of neuron systems. Dynamic regimes of information processing// Proc. Nonlinear Waves–2002 / Eds A.V. Gaponov-Grekhov, V.I. Nekorkin. Nizhny Novgorod. IAP RAS. 2003. P. 90–114 (In Russian).
11. Coenen A.M.L., van Luijtelaar E.L.J.M., Kuznetsova G.D., Ivanov A.E., Nuidel I.V., Khurlapov P.G., and Yakhno V.G. Modeling of transition regimes between normal and pathological transformation of sensor signals in brain // Proceedings of Nijmen- gen Institute for Cognition and Information, 2004. P. 331.
12. Nuidel I.V., Sokolov M.E., Yakhno V.G. Universal scheme of neuron interaction module for functional modeling of information processing// Slozhnost’. Razum. Postneklassika. 2013. N4. (In Russian).
13. Sokolov M.E., Kuznetsova G.D., Nuidel I.V., Yakhno V.G. Modeling of dynamic processes of sensor signal processing in talamo-cortical networks // Izvestiya VUZ. Applied Nonlinear Dynamics. 2011. N6. P. 117–129. (In Russian).
14. Kudryashov A.V., Yakhno V.G. The propagation of areas of increased impulse activity in the neural network // Sbornik: The Dynamics of Biological Systems. 1978. P. 45–59. (In Russian).
15. Belliustin N.S., Kuznetsov S.O., Nuidel I.V., Yakhno V.G. Neural networks with close nonlocal coupling for analysing composite images // Neurocomputing. 1991. Vol. 3. P. 231–246.
16. Kuznetsov S.O., Nuidel I.V., Yakhno V.G. Segmentation and Pattern Recognition of a Composite Image Product by a System of Elements with Neural network Architecture // In book: Neurocomputers and Attention/ Eds A. Holden, V. Kryukov. Manchester University Press. 1991, P. 590–596.
17. Yakhno V.G. Processes of self-organization in distributed neuron systems. Examples of possible applications // «Neiroinformatics–2001». Lectures on neuroinformatics. M.: MEPhI, 2001. P. 103–141 (In Russian).
18. Yakhno V.G., Nuidel I.V., Ivanov A.E. The model neuron system: examples of dynamic processes // In: «Nonlinear Waves - 2004» / Eds A.V. Gaponov-Sin, V.I. Nekorkin. Nizhny Novgorod: IAP RAS, 2005. P. 362–375 (In Russian).
19. Spitcin I.G., Nuidel I.V., Yakhno V.G. Modeling thalamocortical connections in the sensory systems // Scientific session MEPhI–2004. Part 1 «Neuroinformatics–2004». The theory of neural networks. 1. Neyrobiology. Application of Neural Networks 1. P. 145–149. (In Russian).
20. Yoonsuck Choe. The role of temporal parameters in a thalamocortical model of analogy // IEEE Transactions on Neural Networks. Vol. 15, N5, September 2004. P. 1071–1082.
BibTeX
author = {A. V. Kolosov and I. V. Nujdel and V. G. Yakhno },
title = { RESEARCH OF DYNAMIC MODES IN THE MATHEMATICAL MODEL OF ELEMENTARY THALAMOCORTICAL CELL},
year = {2016},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {24},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/research-of-dynamic-modes-in-the-mathematical-model-of-elementary-thalamocortical-cell},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2016-24-5-72-83},pages = {72--83},issn = {0869-6632},
keywords = {Neuronlike network,self-oscillation,relaxation oscillations,epilepsy,inhibitory connections,excitatory connections,signal gating,sensor signal.},
abstract = {In the work the mathematical model of the thalamocortical network’s unit cell and it’s characteristic dynamical modes in system, describing the interaction between a thalamus, thalamus reticular nucleus and a cortex, is studied. During normal information processing, input signal gating occurs in time in the thalamo-cortical network. The violation of the normal functioning leads to an epilepsy, when the perception of information is disrupted. The consideration of this system will lead to an understanding of the human perception’s violation regularities, which correspond to the thalamo-cortical network’s self-oscillation. The focused mathematical model is described by a system of three differential equations. For this system a three-dimensional phase space is constructed, enabling us to track changes of the system’s «equilibrium states» when parameters change. The analysis of the system for the first time is performed using a three-dimensional phase space; the behavior of the representative points’ trajectories is considered, and the representation of equilibrium states of the system becomes obvious. Due to the large number of parameters of the system to build that space makes it easier to predict the development of the system in subsequent time for any parameters. The classification of dynamical modes in system (unexcited, excited and a self-oscillation), depending on the magnitude of the constant external signal incoming to the thalamus, is carried out. It is shown that the response of the system consists of a first pulse and following it self-oscillation pulses, whose period is different from the duration of the first pulse. The dependence of characteristic times of the first impulse response and the period of the self-oscillation with the external signal is studied. The numerical analysis of the model revealed the existence of U-shaped dependence of the first pulse duration and a decreasing of the period of the self-oscillation in the response to the increase of the external signal value. The results are important for further consideration of the plausibility of the hypothesis, according to which the thalamocortical networks control the activity of the areas of the cerebral cortex and focused (normally) on the integration of the obtained results for decision-making at higher levels of neural network processing in brain structures. DOI: 10.18500/0869-6632-2016-24-5-72-83 Paper reference: Kolosov A.V., Nuidel I.V., Yakhno V.G. Research of dynamic modes in the mathematical model of elementary thalamocortical cell. Izvestiya VUZ. Applied Nonlinear Dynamics. 2016. Vol. 24. Issue 5. P. 72–83. Download full version }}