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

For citation:

Postnov D. E., Sosnovtseva O. V., Han S. K. Transition from antiphase to inphase synchronization in coupled neuron models. Izvestiya VUZ. Applied Nonlinear Dynamics, 1999, vol. 7, iss. 1, pp. 88-100. DOI: 10.18500/0869-6632-1999-7-1-88-100

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 1999no1p088.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Journal in the journal
Article type: 
Article
UDC: 
517.958:57
DOI: 
10.18500/0869-6632-1999-7-1-88-100

Transition from antiphase to inphase synchronization in coupled neuron models

Autors: 
Postnov Dmitrij Engelevich, Saratov State University
Sosnovtseva Olga Vladimirovna, Danmarks Tekniske Universitet
Han Seung Kee, Chonbuk National University
Abstract: 

Based on bifurcational analysis we describe the key transitions from antiphase resonance observed for a weak coupling, to inphase synchronization as the parameter of interaction is increased. Role of multistability in the structure of the main synchronization region is studied. Two coupled Moris — Lecar systems are used as a
model.

Key words: 
-
Acknowledgments: 
Co by D.E. Postnov and O.V. Sosnovtseva the work was supported by grants RFBR 98-02-16531 and 99-02-17732. S.K. Han thanks the support of Ministry of Education of the Republic of Korea, BSR(97-2436) program, and Hallum Academy of Sciences (Hallum University, Когеа).
Reference: 
  1. Arbib MA, editor. The handbook of Brain Theory and Neural Networks. Cambridge: MIT Press; 1998. 1134 p.
  2. Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 1952;117(4):500-544. DOI: 10.1113/jphysiol.1952.sp004764.
  3. Abarbanel HD, Rabinovitch MN, Selverston A, Bazhenov MV, Huerta R, Sushchik MM, Rrubchinskii LL. Synchronisation in neural networks. Phys. Usp. 1996;39(4):337-362. DOI: 10.1070/pu1996v039n04abeh000141.
  4. Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 1981;35(1):193–213. DOI: 10.1016/S0006-3495(81)84782-0.
  5. Arnold VI, Afraimovich VS, Ilyashenko YuS, Shilnikov LP. Dynamical Systems V: Bifurcation Theory and Catastrophe Theory. Berlin: Springer; 1994. 274 p. DOI: 10.1007/978-3-642-57884-7.
  6. Sherman А, Rinzel J. Rhythmogenic effects of weak electronic coupling in neuronal models. Рrос. Natl. Acad. Sci. USA. 1992;89(6):2471-2474. DOI: 10.1073/pnas.89.6.2471.
  7. Наn SK, Kurrer C, Kuramoto Y. Dephasing and bursting in coupled neural oscillators. Phys. Rev. Lett. 1995;75(17):3190-3193. DOI: 10.1103/PhysRevLett.75.3190.
  8. Postnov DE, Наn SK. The mechanism of counterphase synchronisation in neuron models. Tech. Phys. Lett. 1999;25(4):11-18. (in Russian).
  9. Postnov DE, Наn SK, Kook H. Synchronization оf diffusively coupled oscillators near the homoclinic bifurcations. Phys. Rev. E. 1999;60(3):2799-2807. DOI: 10.1103/PhysRevE.60.2799.
  10. Guckenheimer J, Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations оf Vector Fields. New York: Springer; 1983. 462 p. DOI: 10.1007/978-1-4612-1140-2.
  11. Rand RH, Holmes PJ. Bifurcation оf periodic motions in two weakly coupled Van der Pol oscillators. Int. J. Nonlin. Mech. 1980;15(4-5):387-399. DOI: 10.1016/0020-7462(80)90024-4.
  12. Aronson DG, Doedel EJ, Othmer HG. An analytical and numerical study of the bifurcation in a system of linearly—coupled oscillators. Physica D. 1987;25(1-3):20-104. DOI: 10.1016/0167-2789(87)90095-9.
  13. Kevrekidis IG, Schmidt LD, Aris R. Some common features оf periodically forced reacting systems. Chemical Engeneering Science. 1986;41(5):1263-1276. DOI: 10.1016/0009-2509(86)87099-3.
  14. Kevrekidis IG, Aris R, Schmidt LD. Forcing аn entire bifurcation diagram: case studies in chemical oscillators. Physica D. 1986;23(1-3):391-395. DOI: 10.1016/0167-2789(86)90145-4.
  15. Taylor МА, Kevrekidis IG. Some common dynamic features оf coupled reacting systems. Physica D. 1991;51(1-3):274-292. DOI: 10.1016/0167-2789(91)90239-6.
  16. Knudsen C, Sturis J, Thomsen JS. Generic bifurcation structures of Arnol’d tongues in forced oscillators. Phys. Rev. А. 1991;44(6):3503-3510. DOI: 10.1103/PhysRevA.44.3503.
  17. Afraimovich VS, Shilnikov LP. Invariant two-dimensional toruses, their destruction and stochasticity. In: Methods of Qualitative Theory of Differential Equations. Gorky: Gorky University Publishing; 1983. P. 3-26. (in Russian).
  18. Anishchenko VS. Complex oscillations in simple systems. М.: Nauka; 1990. 312 p. (in Russian).
  19. Volkov ЕI, Romanov VA. Bifurcations in the system оf two identical diffusively coupled brusselators. Physica Scripta. 1995;51(1):19-28. DOI: 10.1088/0031-8949/51/1/004.
  20. Stolyarov MN, Romanov VA, Volkov EI. Out—of—phase mixed—mode oscillations of two strongly coupled identical relaxation oscillators. Phys.Rev.E. 1996;54(1):163-169. DOI: 10.1103/PhysRevE.54.163.
Received: 
15.03.1999
Accepted: 
12.05.1999
Published: 
28.05.1999
  • 269 reads