PapersNo Access

PROPAGATING INTERFACES IN A TWO-LAYER BISTABLE NEURAL NETWORK

Institute of Applied Physics of Russian Academy of Science, 46 Uljianov Str., 603950 Nizhny Novgorod, Russia

Laboratoire LE2I UMR Cnrs 5158, Aile des Sciences de l'ingénieur, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France

Search for more papers by this author

J. M. BILBAULT

Laboratoire LE2I UMR Cnrs 5158, Aile des Sciences de l'ingénieur, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France

Search for more papers by this author

, and

P. MARQUIÉ

Laboratoire LE2I UMR Cnrs 5158, Aile des Sciences de l'ingénieur, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France

Search for more papers by this author

https://doi.org/10.1142/S0218127406015003Cited by:1 (Source: Crossref)

Abstract

The dynamics of propagating interfaces in a bistable neural network is investigated. We consider the network composed of two coupled 1D lattices and assume that they interact in a local spatial point (pin contact). The network unit is modeled by the FitzHugh–Nagumo-like system in a bistable oscillator mode. The interfaces describe the transition of the network units from the rest (unexcited) state to the excited state where each unit exhibits periodic sequences of excitation pulses or action potentials. We show how the localized inter-layer interaction provides an "excitatory" or "inhibitory" action to the oscillatory activity. In particular, we describe the interface propagation failure and the initiation of spreading activity due to the pin contact. We provide analytical results, computer simulations and physical experiments with two-layer electronic arrays of bistable cells.

Keywords:

References

A. R. A. Anderson and B. D. Sleeman, Int. J. Bifurcation and Chaos 5, 63 (1995). Link, Web of Science, Google Scholar
S. Binczaket al., Electron. Lett. 34, 1061 (1998). Web of Science, Google Scholar
R. Borisyuk and F. Hoppenstadt, Biol. Cybern. 81, 359 (1999). Web of Science, Google Scholar
P. C. Bressloff and S. Coombes, Physica D 130, 232 (1999). Web of Science, Google Scholar
P. C. Bressloff, Physica D 155, 83 (2001). Web of Science, Google Scholar
J. Brindley , A. V. Holden and A. Palmer , Nonlinear Wave Processes in Excitable Media , ed. A. V. Holden ( Plenum Press , NY , 1991 ) . Google Scholar
J. C. Comte, S. Morfu and P. Marquié, Phys. Rev. E 64, 027102 (2001). Web of Science, Google Scholar
S. Coombes, Math. Biosci. 170, 155 (2001). Web of Science, Google Scholar
B. Ermentrout, X. Chen and Z. Chen, Physica D 108, 147 (1997). Web of Science, Google Scholar
T. Erneux and G. Nicolis, Physica D 67, 237 (1993). Web of Science, Google Scholar
D. Golomb and Y. Amitai, J. Neurophysiol. 78, 1199 (1997). Web of Science, Google Scholar
D. Golomb and G. B. Ermentrout, Proc. Natl. Acad. Sci. USA 96, 13480 (1999). Web of Science, Google Scholar
F. C. Hoppenstadt and H. D. Mittelmann, J. Math. Biol. 35, 988 (1997). Web of Science, Google Scholar
V. B. Kazantsev, Phys. Rev. E 64, 056210-1 (2001), DOI: 10.1103/PhysRevE.64.056210. Web of Science, Google Scholar
J. P. Keener, SIAM J. Appl. Math. 47, 556 (1987). Web of Science, Google Scholar
J. P. Keener, Physica D 136, 1 (2000). Web of Science, Google Scholar
P. Kudela, P. J. Franaszczuk and G. K. Bergey, Neurocomputing 26–27, 411 (1999). Web of Science, Google Scholar
Y. Kuramoto , Chemical Oscillations, Waves and Turbulence ( Springer-Verlag , Berlin , 1989 ) . Google Scholar
J.-W. Lamet al., J. Neurosci. 20, 749 (2000). Web of Science, Google Scholar
R. S. MacKay and J.-A. Sepulchre, Physica D 82, 243 (1995). Web of Science, Google Scholar
S. Morfuet al., Phys. Rev. E 66, 046127 (2002). Web of Science, Google Scholar
J. D. Murray , Mathematical Biology ( Springer-Verlag , Berlin , 1988 ) . Google Scholar
V. I. Nekorkinet al., Physica D 100, 330 (1997). Web of Science, Google Scholar
V. I. Nekorkinet al., Phys. Rev. E 57, 3344 (1998). Web of Science, Google Scholar
V. I. Nekorkinet al., Phys. Rev. E 64, 036602-1 (2001), DOI: 10.1103/PhysRevE.64.036602. Web of Science, Google Scholar
R. Osan and B. Ermentrout, Neurocomputing 38, 789 (2001). Web of Science, Google Scholar
R. Osan and B. Ermentrout, Physica D 163, 217 (2002). Web of Science, Google Scholar
A. Peinado, J. Neurosci. 20, RC54 (2000). Google Scholar
J. C. Prechtlet al., Proc. Natl. Acad. Sci. USA 94, 7621 (1997). Web of Science, Google Scholar
A. Scott , Nonlinear Science: Emergence and Dynamics of Coherent Structures ( Oxford University Press , Oxford , 1998 ) . Google Scholar
R. M. Siegel and H. L. Read, Neural Networks 14, 697 (2001). Web of Science, Google Scholar
J.-J., Wu, L. Guan and Y. Tsau, J. Neurosci. 19, 5005 (1999). Web of Science, Google Scholar
B. Zinner, SIAM J. Appl. Math. 22, 1016 (1991). Web of Science, Google Scholar
B. Zinner, J. Diff. Eq. 96, 1 (1992). Web of Science, Google Scholar