Low-dimensional model for adaptive networks of spiking neurons
We investigate a large ensemble of quadratic integrate-and-fire neurons with heterogeneous input currents and adaptation variables. Our analysis reveals that, for a specific class of adaptation, termed quadratic spike-frequency adaptation, the high-dimensional system can be exactly reduced to a low-...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/424674 |
| Online Access: | https://hdl.handle.net/2117/424674 https://dx.doi.org/10.1103/PhysRevE.111.014422 |
| Access Level: | Open access |
| Keyword: | Neuronal dynamics Spiking neurons Synchronization Collective dynamics Coupled oscillators Integrate-and-fire model Mean field theory Neuronal network models Spiking neuron models Àrees temàtiques de la UPC::Enginyeria biomèdica |
| Summary: | We investigate a large ensemble of quadratic integrate-and-fire neurons with heterogeneous input currents and adaptation variables. Our analysis reveals that, for a specific class of adaptation, termed quadratic spike-frequency adaptation, the high-dimensional system can be exactly reduced to a low-dimensional system of ordinary differential equations, which describes the dynamics of three mean-field variables: the population's firing rate, the mean membrane potential, and a mean adaptation variable. The resulting low-dimensional firing rate equations (FREs) uncover a key generic feature of heterogeneous networks with spike-frequency adaptation: Both the center and width of the distribution of the neurons' firing frequencies are reduced, and this largely promotes the emergence of collective synchronization in the network. Our findings are further supported by the bifurcation analysis of the FREs, which accurately captures the collective dynamics of the spiking neuron network, including phenomena such as collective oscillations, bursting, and macroscopic chaos. |
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