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J. Rinzel (1987)
A Formal Classification of Bursting Mechanisms in Excitable Systems
V.N. Belykh, Yu. S. Chertkov (1980)
Boundary Value Problems
I. Belykh, M. Hasler, M. Lauret, H. Nijmeijer (2005)
Synchronization and Graph TopologyInt. J. Bifurc. Chaos, 15
L. Pecora, T. Carroll (1998)
Master Stability Functions for Synchronized Coupled SystemsPhysical Review Letters, 80
(1980)
Periodic Motion of Special Type in Differential Equations the 3rd Order with a Small Parameter, in Boundary Value Problems, Perm: Perm
Pogromskiy (2005)
Cooperative oscillatory behavior of mutually coupled dynamical systems
K. Chergui, P. Charlety, Hideo Akaoka, C. Saunier, J. Brunet, Michel Buda, Torgny Svensson, Guy Chouvet (1993)
Tonic Activation of NMDA Receptors Causes Spontaneous Burst Discharge of Rat Midbrain Dopamine Neurons In VivoEuropean Journal of Neuroscience, 5
C. Vozzi, Susanne Ullrich, A. Charollais, Jacques Philippe, L. Orci, Paolo Meda (1995)
Adequate connexin-mediated coupling is required for proper insulin productionThe Journal of Cell Biology, 131
Victor Kazantsev, S. Asatryan (2011)
Bistability induces episodic spike communication by inhibitory neurons in neuronal networks.Physical review. E, Statistical, nonlinear, and soft matter physics, 84 3 Pt 1
A. Gjurchinovski, A. Zakharova, E. Schöll (2013)
Amplitude death in oscillator networks with variable-delay coupling.Physical review. E, Statistical, nonlinear, and soft matter physics, 89 3
J. Wojcik, A. Shilnikov (2015)
Nonlinear Dynamics New Directions: Models and Applications
I. Quesada, E. Fuentes, E. Andreu, P. Meda, A. Nadal, B. Soria (2003)
On-line analysis of gap junctions reveals more efficient electrical than dye coupling between islet cells.American journal of physiology. Endocrinology and metabolism, 284 5
A. Prasad, M. Dhamala, B. Adhikari, R. Ramaswamy (2010)
Amplitude death in nonlinear oscillators with nonlinear coupling.Physical review. E, Statistical, nonlinear, and soft matter physics, 81 2 Pt 2
Ruiqi Wang, Luonan Chen (2005)
Synchronizing Genetic Oscillators by Signaling MoleculesJournal of Biological Rhythms, 20
C. Wu, L. Chua (1996)
On a conjecture regarding the synchronization in an array of linearly coupled dynamical systemsIEEE Transactions on Circuits and Systems I-regular Papers, 43
J. Pitts, M. Finbow (1986)
The Gap JunctionJournal of Cell Science, 1986
Ch.W. Wu, L. O. Chua (1996)
On a Conjecture Regarding the Synchronization in an Array of Linearly Coupled Dynamical SystemsIEEE Trans. Circuits Syst. 1, 43
V. Resmi, G. Ambika, R. Amritkar, G. Rangarajan (2012)
Amplitude death in complex networks induced by environment.Physical review. E, Statistical, nonlinear, and soft matter physics, 85 4 Pt 2
Nalin Kumar, N. Gilula (1996)
The Gap Junction Communication ChannelCell, 84
C. Negro, C. Hsiao, S. Chandler, A. Garfinkel (1998)
Evidence for a novel bursting mechanism in rodent trigeminal neurons.Biophysical journal, 75 1
Renato Mirollo, S. Strogatz (1990)
Amplitude death in an array of limit-cycle oscillatorsJournal of Statistical Physics, 60
“Subcritical Elliptic Bursting of Bautin Type ” (Izhikevich (2000b)). The following
I. Belykh, M. Hasler, M. Lauret, H. Nijmeijer (2005)
Synchronization and Graph TopologyInternat. J. Bifur. Chaos Appl. Sci. Engrg., 15
F. Caserta, Robert Hausman, W. Eldred, C. Kimmel, H. Stanley (1992)
Effect of viscosity on neurite outgrowth and fractal dimensionNeuroscience Letters, 136
V.N. Belykh, E.V. Pankratova, E. Mosekilde (2008)
Dynamics and Synchronization of Noise Perturbed Ensembles of Periodically Activated Neuron CellsInternat. J. Bifur. Chaos Appl. Sci. Engrg., 18
J. Wojcik, A. Shilnikov (2013)
Voltage Interval Mappings for an Elliptic Bursting ModelPhysica D: Nonlinear Phenomena
E. Camacho, R. Rand, H. Howland (2004)
Dynamics of two van der Pol oscillators coupled via a bathInternational Journal of Solids and Structures, 41
E. Sykova, C. Nicholson (2008)
Diffusion in brain extracellular space.Physiological reviews, 88 4
Arthur Freeman, Leonard Meltzer, Benjamin Bunney (1985)
Firing properties of substantia nigra dopaminergic neurons in freely moving rats.Life sciences, 36 20
A. Ponzi, J. Wickens (2010)
Sequentially Switching Cell Assemblies in Random Inhibitory Networks of Spiking Neurons in the StriatumThe Journal of Neuroscience, 30
R. Ham, W. Mckeehan (1979)
Media and growth requirements.Methods in enzymology, 58
E.M. Izhikevich (2001)
Synchronization of Elliptic BurstersSIAM Rev., 43
G. Katriel (2008)
Synchronization of oscillators coupled through an environmentPhysica D: Nonlinear Phenomena, 237
V. Belykh, E. Pankratova, E. Mosekilde (2008)
Dynamics and Synchronization of Noise perturbed Ensembles of Periodically activated Neuron CellsInt. J. Bifurc. Chaos, 18
E. Vigmond, J. Velazquez, T. Valiante, B. Bardakjian, P. Carlen (1997)
Mechanisms of electrical coupling between pyramidal cells.Journal of neurophysiology, 78 6
V. Belykh, E. Pankratova (2006)
Chaotic synchronization in ensembles of coupled neurons modeled by the FitzHugh-Rinzel systemRadiophysics and Quantum Electronics, 49
A. Komendantov, Olena Komendantova, Steven Johnson, C. Canavier (2004)
A modeling study suggests complementary roles for GABAA and NMDA receptors and the SK channel in regulating the firing pattern in midbrain dopamine neurons.Journal of neurophysiology, 91 1
J. Rinzel (1987)
Mathematical Topics in Population Biology, Morphogenesis and Neurosciences: Proc. of the Internat. Symp. (Kyoto, November 10–15, 1985): Vol. 3
We study the dynamics of multielement neuronal systems taking into account both the direct interaction between the cells via linear coupling and nondiffusive cell-to-cell communication via common environment. For the cells exhibiting individual bursting behavior, we have revealed the dependence of the network activity on its scale. Particularly, we show that small-scale networks demonstrate the inability to maintain complicated oscillations: for a small number of elements in an ensemble, the phenomenon of amplitude death is observed. The existence of threshold network scales and mechanisms causing firing in artificial and real multielement neural networks, as well as their significance for biological applications, are discussed.
Regular and Chaotic Dynamics – Springer Journals
Published: Mar 23, 2017
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