Free Access
Issue
Math. Model. Nat. Phenom.
Volume 7, Number 6, 2012
Biological oscillations
Page(s) 67 - 94
DOI https://doi.org/10.1051/mmnp/20127604
Published online 12 December 2012
  1. W.C. Abraham. Metaplasticity: tuning synapses and networks for plasticity. Nature Reviews Neuroscience, 9 (2008), 387–399. [CrossRef] [PubMed] [Google Scholar]
  2. T. Bem, J. Rinzel. Short duty cycle destabilizes a half-center oscillator, but gap junctions can restabilize the anti-phase pattern. Journal of Neurophysiology, 91 (2004), 693–703. [CrossRef] [PubMed] [Google Scholar]
  3. M.A. Diana, P. Bregestovski. Calcium and endocannabinoids in the modulation of inhibitory synaptic transmission. Cell Calcium, 37 (2005), 497–505. [CrossRef] [PubMed] [Google Scholar]
  4. A. Dityatev, D.A. Rusakov. Molecular signals of plasticity at the tetrapartite synapse. Current Opinion in Neurbiology, 21 (2011), 353–359. [CrossRef] [Google Scholar]
  5. W. Gerstner, R. Kempter, J.L. van Hemmen, H. Wagner. A neuronal learning rule for sub-millisecond temporal coding. Nature, 386 (1996), 76–78. [CrossRef] [PubMed] [Google Scholar]
  6. J. Guckenheimer, P. Holmes. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer-Verlag, 1986. [Google Scholar]
  7. S.Yu. Gordleeva, S.V. Stasenko, A.V. Semyanov, A.E. Dityatev, V.B. Kazantsev Bi-directional astrocytic regulation of neuronal activity within a network. Frontiers of Computational Neuroscience, 6 (2012), article 92. [Google Scholar]
  8. F.C. Hoppensteadt, E.M. Izhikevich. Weakly connected neural networks. Springer-Verlag, 1997. [Google Scholar]
  9. Y. Ikegaya, G. Aaron, R. Cossart, D. Aronov, I. Lampl, D. Ferster, R. Yuste. Synfire chains and cortical songs: Temporal modules of cortical activity. Science, 304 (2004), 559–564. [CrossRef] [PubMed] [Google Scholar]
  10. E.M. Izhikevich. Polychronization: Computation with spikes. Neural Computation, 18 (2006), 245–282. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  11. E.M. Izhikevich. Dynamical systems in neuroscience. The geometry of excitability and bursting. MIT Press, 2007. [Google Scholar]
  12. E.M. Izhikevich. Solving the distal reward problem through linkage of STDP and dopamine signaling. Cerebral Cortex, 17 (2007), 2443–2452. [CrossRef] [Google Scholar]
  13. C. Kayser, M.A. Montemurro, N.K. Logothetis, S. Panzeri. Spike-phase coding boosts and stabilizes information carried by spatial and temporal spike patterns. Neuron, 61 (2009), 597–608. [CrossRef] [PubMed] [Google Scholar]
  14. V. Kazantsev, I. Tyukin. Adaptive and phase selective spike timing dependent plasticity in synaptically coupled neuronal oscillators. PLOS ONE, 7 (2012), e30411. [CrossRef] [PubMed] [Google Scholar]
  15. V. Kazantsev, S.Yu. Gordleeva, S.V. Stasenko, A.E. Dityatev. A homeostatic model of neuronal firing governed by feedback signals from extracellular matrix. PLOS ONE, 7 (2012), e41646. [CrossRef] [PubMed] [Google Scholar]
  16. V.B. Kazantsev, V.I. Nekorkin, S. Binczak, S. Jacquir, J.M. Bilbault. Spiking dynamics of interacting oscillatory neurons. Chaos, 15 (2005), 023103. [CrossRef] [Google Scholar]
  17. H.J. Koester, B. Sakmann. Calcium dynamics in single spines during coincident pre- and postsynaptic activity depend on relative timing of back-propagating action potentials and subthreshold excitatory postsynaptic potentials. Proc Natl Acad Sci USA, 95 (1998), 9596–9601. [CrossRef] [Google Scholar]
  18. F. Lanore, N. Rebola, M. Carta. Spike-timing-dependent plasticity induces presynaptic changes at immature hippocampal mossy fiber synapses. The Journal of Neuroscience, 29 (2009), 8299–8301. [CrossRef] [Google Scholar]
  19. T. Ohno-Shosakua, Y. Hashimotodania, T. Maejima, M. Kano. Calcium signaling and synaptic modulation: Regulation of endocannabinoid-mediated synaptic modulation by calcium. Cell Calcium, 38 (2005), 369–374. [CrossRef] [PubMed] [Google Scholar]
  20. A. Pikovsky, M. Rosenblum, J. Kurths. Synchronization: a unified concept in nonlinear sciences. Cambridge University Press, 2001. [Google Scholar]
  21. J.D. Rolston, S.M. Wagenaar, D.A.and Potter. Precisely timed spatiotemporal patterns of neural activity in dissociated cortical cultures. Neuroscience, 148 (2007), 294–303. [CrossRef] [PubMed] [Google Scholar]
  22. P.F. Rowat, A.I. Selverston. Modeling the gastric mill central pattern generator with a relaxation-oscillator network. Journal of Neurophysiology, 70 (1993), 1030–1053. [PubMed] [Google Scholar]
  23. L.P. Shilnikov, A.L. Shilnikov, D.V. Turaev, L.O. Chua. Methods of qualitative theory in nonlinear dynamics. World Scientific, 2001. [Google Scholar]
  24. P.J. Sjostrom, E.A. Rancz, A. Roth, M. Hausser. Dendritic excitability and synaptic plasticity. Physiological Reviews, 88 (2008), 769–840. [CrossRef] [PubMed] [Google Scholar]
  25. S. Song, K.D. Miller, L.F. Abbott. Competitive Hebbian learning through spike-timing-dependent synaptic plasticity. Nature Neuroscience, 3 (2000), 919–926. [CrossRef] [PubMed] [Google Scholar]
  26. I. Tyukin. Adaptation in dynamical systems. Cambridge University Press, 2011. [Google Scholar]
  27. I. Tyukin, E. Steur, H. Neijmeijer, C. van Leeuwen. Small-gain theorems for systems with unstable invariant sets. SIAM Journal on Control and Optimization, 47 (2008), 849–882. [CrossRef] [MathSciNet] [Google Scholar]
  28. A. Whitehead, M.I. Rabinovich, R. Huerta, V.P. Zhigulin, H.D.I. Abarbanel. Dynamical synaptic plasticity: a model and connection to some experiments. Biological Cybernetics, 88 (2003), 229–235. [CrossRef] [PubMed] [Google Scholar]

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