The influence of noise on synchronous dynamics in a diluted neural network |
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| Institution: | 1. Dipartimento di Fisica, via G.P. Usberti, 7/A, I-43124 Parma, Italy;2. Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, via Sansone, 1, I-50019 Sesto Fiorentino, Italy;3. INFN Sez. Milano Bicocca, Gruppo Collegato di Parma, via G.P. Usberti, 7/A, I-43124 Parma, Italy;4. Dipartimento di Fisica, via Sansone, 1, I-50019 Sesto Fiorentino, Italy;5. Istituto dei Sistemi Complessi, CNR, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy;6. INFN Sez. Firenze, via Sansone, 1, I-50019 Sesto Fiorentino, Italy;1. Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China;2. Institute of Physics, Humboldt-Universität zu Berlin, Germany;1. Electrical and Computer Engineering Department, George Mason University, 4400 University Dr. MSN 1G5, Fairfax, VA 22030, USA;2. Electrical Engineering Department, University of South Florida, 4202 East Fowler Avenue, ENB118, Tampa, FL 33620, USA;3. Department of Molecular Neuroscience, Krasnow Institute for Advanced Study, George Mason University, 4400 University Dr. MSN 2A1, Fairfax, VA 22030, USA;4. Department of Bioengineering, George Mason University, 4400 University Dr. MSN 1G5, Fairfax, VA 22030, USA;1. Dept. of Mathematical Analysis, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic;2. Dept. of Geoinformatics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic;1. RIKEN Brain Science Institute, Wako, Saitama 351-0198, Japan;2. University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia;1. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, PR China;2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, PR China;1. Progressive Science Institute, 2233 Ala Wai Blvd 3C, Honolulu, HI 96815, USA;2. Speedstat, 19 Langstrom Crescent, Ottawa, Ontario K1G 5J5, Canada;3. Department of Earth Sciences, Carleton University, Ottawa, Ontario K1S 5B6, Canada;4. Progressive Science Institute, Box 5335, Berkeley, CA 94705, USA |
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| Abstract: | We study the influence of noise on the dynamics of a simple model of excitatory leaky integrate – and – fire neurons in a diluted network. The stochastic process amounts to a random walk with boundaries acting on the external current, whose average value plays the role of a control parameter identifying different dynamical phases. Above a given threshold value one observes a gaussian statistics of synchronous firing events, that changes to an asymmetric long-tail distribution below threshold. For uncorrelated noise the distribution below threshold exhibits an exponential tail for large rare events, while for strongly correlated noise the long-tail turns to a power-law. This interesting dynamical scenario is shown to persist also when short-term plasticity is introduced in the model. Synchronous firing events change to population bursts and the model with plasticity is shown to reproduce quantitatively what observed in in vitro experiments. We also discuss the persistence of this scenario in the thermodynamic limit. |
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