ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Andreev K. V., Krasichkov L. V. Sаmе peculiarities оf synchronization under changing thе connection structure in small model neuron ensembles, described by piecewise continuous maps and piecewise discontinuous maps. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 4, pp. 82-94. DOI: 10.18500/0869-6632-2002-10-4-82-94

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
53.072:51
DOI: 
10.18500/0869-6632-2002-10-4-82-94

Sаmе peculiarities оf synchronization under changing thе connection structure in small model neuron ensembles, described by piecewise continuous maps and piecewise discontinuous maps

Autors: 
Andreev Kirill Vladimirovich, Saratov State University
Krasichkov L. V., Saratov State University
Abstract: 

The piecewise-linear stochastic map, the piecewise-continuous dynamic map and piecewise-discontinuous dynamic map, for electrical activity modeling of neuron are proposed. These maps are constructed using the phenomenological notions of biological neuron dynamics. Advantages and limitations of the proposed maps are discussed. The behaviour оf small model neuron ensembles оn the parameters plane is investigated. Considerable dependence between the synchronization degree and the topology of neuron ensemble is shown.

Key words: 
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Acknowledgments: 
The work was carried out with the support of the RFBR, grant number 02-02-16351, 00-15-96673, the Ministry of Education of the Russian Federation, grant № E00-3.5-196 and CRDF, REC-006.
Reference: 
  1. Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal оf Physiology (London). 1952;117(4):500-544. DOI: 10.1113/jphysiol.1952.sp004764.
  2. FitzHugh R. Impulses and physiological states in models оf nerve membrane. Biophysics Journal. 1961;1(6):445-466. DOI: 10.1016/S0006-3495(61)86902-6.
  3. Nagumo J, Arimoto S, Yoshizawa S. An active pulse transmission line simulating nerve axon. Proc. IRE. 1962;50(10):2061-2070. DOI: 10.1109/JRPROC.1962.288235.
  4. Abarbanel HD, Rabinovich MI, Selverston A, Bazhenov MV, Huerta R, Sushchik MM, Rubchinskii LL. Synchronisation in neural networks. Phys. Usp. 1996;39(4):337-362. DOI: 10.1070/PU1996v039n04ABEH000141.
  5. Abarbanel HDI, Huerta К, Rabinovich МI, Rowat PF, Rulkov NF, Selverston Al. Synchronized action of synaptically coupled chaotic models neurons. Neural Computation. 1996;8(8):1567-1602. DOI: 10.1162/neco.1996.8.8.1567.
  6. Huerta В. A finite automata model оf spiking-bursting neurons. International Journal of Bifurcation аnd Chaos. 1996;6(4):705-714. DOI: 10.1142/S0218127496000369.
  7. Rabinovich ML, Selverston AL, Rubchinsky L, Huerta R. Dynamics and kinematics оf simple neural systems. Chaos. 1996;6(3):288-296. DOI: 10.1063/1.166176.
  8. Belykh IV. Bifurcations of oscillations of the membrane potential and the use of mappings for modeling electrically coupled neurons. Radiophys. Quantum Electron. 1998;41(12):1066-1071. DOI: 10.1007/BF02676504.
  9. Hayakawa Y, Sawada Y. Learning-induced synchronization оf а globally coupled excitable map system. Physical Review E. 2000;61(5):5091-5097. DOI: 10.1103/physreve.61.5091.
  10. Rulkov NF. Regularization оf synchronized chaotic bursts. Physical Review Letters. 2001;86(1):183-186. DOI: 10.1103/physrevlett.86.183.
  11. Elson RC, Selverston AL, Huerta R, Rulkov NF, Rabinovich MI, Abarbanel HDI. Synchronous behavior оf two coupled biological neurons. Physical Review Letters. 1998;81(25):5692-5695. DOI: 10.1103/PhysRevLett.81.5692.
  12. Szucs А, Varona Р, Volkovskii AR, Abarbanel НDI, Rabinovich MI, Selverston AI. Interacting biological and electronic neurons generate realistic oscillatory rhythms. Neuro Report. 2000;11(3):563-569. DOI: 10.1097/00001756-200002280-00027.
  13. Andreev KV, Krasichkov LV. Modeling the behavior of a neuron using functional mapping. In: Second International Conference “Fundamental Problems of Physics” (Saratov, Russia, October 9-14, 2000). Conference Materials. Saratov: “College”; 2000. P. 28 (in Russian).
  14. Andreev KV. Model of electrical activity of a neuron in the form of a functional display. In: “Nonlinear Days in Saratov for Young People - 2000”. Collection of Materials from the Scientific School-Conference. Saratov: “College”; 2000. P. 76 (in Russian).
Received: 
01.08.2002
Accepted: 
10.09.2002
Available online: 
19.01.2024
Published: 
30.12.2002
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