Stable chaos in fluctuation driven neural circuits |
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| Institution: | 1. CNR – Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy;2. INFN Sez. Firenze, via Sansone, 1, I-50019 Sesto Fiorentino, Italy;1. Center of Excellence for Functional Materials, Laboratory of Physical Chemistry, Åbo Akademi University, Porthaninkatu 3-5, FI-20500 Turku, Finland;2. Center of Excellence for Functional Materials, Laboratory of Paper Coating and Converting, Åbo Akademi University, Porthaninkatu 3-5, FI-20500 Turku, Finland;3. Laboratory of Inorganic Chemistry, University of Ulm, 87031 Ulm Albert Einstein Allee II, Germany;1. Dipartimento di Matematica, La Sapienza Universita di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy;2. Mathematics, Division of Science, New York University Abu Dhabi, United Arab Emirates;1. Crete Center for Quantum Complexity & Nanotechnology, Department of Physics, University of Crete, 71003 Heraklion, Greece;2. Department of Physics, Faculty of Science, Ege University, 35100 Izmir, Turkey;3. Istanbul University, Science Faculty, Physics Department, 34134 Istanbul, Turkey;4. Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, 71110 Heraklion, Greece;5. Department of Physics, School of Science and Technology, Nazarbayev University, 53 Kabanbay Batyr Ave., Astana 010000, Kazakhstan;1. Institute of Low Temperature Science, Hokkaido University, N19W8, Kita-ku, Sapporo 060-0819, Japan;2. Department of Natural History Sciences, Faculty of Science, Hokkaido University, N10W8, Kita-ku, Sapporo 060-0810, Japan;1. Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Nanjing University, 210093 Nanjing, China;2. State Key Laboratory of Resources and Environmental Information System, Chinese Academy of Sciences, 100101 Beijing, China;3. Changjiang River Scientific Research Institute, Changjiang Water Resources Commission, 430010 Wuhan, China;1. Department of Reproductive Biology, Yazd Institute for Reproductive Sciences, Shahid Sadoughi University of Medical Sciences, Yazd, Iran;2. Department of Gynecology, Yazd Institute for Reproductive Sciences, Shahid Sadoughi University of Medical Sciences, Yazd, Iran;3. Department of Life, Health and Environmental Sciences, University of L’Aquila, L’Aquila, Italy |
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| Abstract: | We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare mean versus fluctuations driven networks, the former (latter) is realized by considering purely excitatory (inhibitory) sparse neural circuits. In the excitatory case the instabilities of the system can be completely captured by an usual linear stability (Lyapunov) analysis, whereas the inhibitory networks can display the coexistence of linear and nonlinear instabilities. The nonlinear effects are associated to finite amplitude instabilities, which have been characterized in terms of suitable indicators. For inhibitory coupling one observes a transition from chaotic to non chaotic dynamics by decreasing the pulse-width. For sufficiently fast synapses the system, despite showing an erratic evolution, is linearly stable, thus representing a prototypical example of stable chaos. |
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