Block structured dynamics and neuronal coding.

When certain control parameters of nervous cell models are varied, complex bifurcation structures develop in which the dynamical behaviors available appear classified in blocks, according to criteria of dynamical likelihood. This block structured dynamics may be a clue to understand how activated neurons encode information by firing spike trains of their action potentials.

[1]  J. M. Gonzalez-Miranda,et al.  Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model. , 2003, Chaos.

[2]  Pengliang Shi,et al.  Noise-induced synchronization in realistic models. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  R. Holzner,et al.  Progress in the analysis of experimental chaos through periodic orbits , 1994 .

[4]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[5]  L. Maler,et al.  Negative Interspike Interval Correlations Increase the Neuronal Capacity for Encoding Time-Dependent Stimuli , 2001, The Journal of Neuroscience.

[6]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[7]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[8]  Teresa Ree Chay,et al.  Chaos in a three-variable model of an excitable cell , 1985 .

[9]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[10]  S. W. Kuffler,et al.  Effect of nerve impulses on the membrane potential of glial cells in the central nervous system of amphibia. , 1966, Journal of neurophysiology.

[11]  Stefan Reinker,et al.  Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons , 2003, Bulletin of mathematical biology.

[12]  R. D. Pinto,et al.  Reliable circuits from irregular neurons: A dynamical approach to understanding central pattern generators , 2000, Journal of Physiology-Paris.

[13]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[14]  M C Eguia,et al.  Information transmission and recovery in neural communications channels. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  M. Rosenblum,et al.  Controlling synchronization in an ensemble of globally coupled oscillators. , 2004, Physical review letters.

[16]  E E Fetz,et al.  Temporal Coding in Neural Populations? , 1997, Science.

[17]  Yuji Ikegaya,et al.  Synfire Chains and Cortical Songs: Temporal Modules of Cortical Activity , 2004, Science.

[18]  André Longtin,et al.  Noise shaping by interval correlations increases information transfer. , 2004, Physical review letters.

[19]  Mingzhou Ding,et al.  Transitions to synchrony in coupled bursting neurons. , 2004, Physical review letters.

[20]  J. Rogers.  Chaos , 1876 .

[21]  D Ferster,et al.  Cracking the Neuronal Code , 1995, Science.

[22]  Arun V. Holden.  Signal processing: Neural coding by correlation? , 2004, Nature.

[23]  Terrence J. Sejnowski,et al.  Time for a new neural code? , 1995, Nature.

[24]  P. Haydon.  Glia: listening and talking to the synapse , 2001, Nature Reviews Neuroscience.

[25]  S. W. Kuffler,et al.  Physiological properties of glial cells in the central nervous system of amphibia. , 1966, Journal of neurophysiology.

[26]  Henry D. I. Abarbanel,et al.  Spike-train bifurcation scaling in two coupled chaotic neurons , 1997 .

[27]  Martin Hasler,et al.  Synchronization of bursting neurons: what matters in the network topology. , 2005, Physical review letters.

[28]  J. Rinzel,et al.  Emergence of organized bursting in clusters of pancreatic beta-cells by channel sharing. , 1988, Biophysical journal.