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Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
Published on: March 2, 2015
A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics
1INRIA, 2004 Route des Lucioles, 06902 Sophia-Antipolis, France. bruno.cessac@inln.cnrs.fr
Journal of Mathematical Biology
|September 18, 2007
Summary
This study analyzes a discrete time spiking neuron model, revealing a link between membrane potential dynamics and spike patterns. The model shows sensitivity to initial conditions, leading to behavior resembling chaos.
Area of Science:
- Computational Neuroscience
- Theoretical Neuroscience
- Dynamical Systems
Background:
- Spiking neuron models are fundamental to understanding neural computation.
- Discrete time models offer computational advantages but require rigorous analysis.
- The Soula et al. model (2006) provides a framework for studying neuronal dynamics.
Purpose of the Study:
- To rigorously analyze the asymptotic dynamics of a discrete time spiking neuron model.
- To establish a correspondence between membrane potential dynamics and spike patterns.
- To investigate the influence of model parameters on neuronal behavior.
Main Methods:
- Symbolic dynamic techniques were employed for mathematical analysis.
- Asymptotic dynamics were derived to understand long-term behavior.
- Numerical experiments were conducted to observe emergent dynamics.
Main Results:
- A one-to-one correspondence was found between membrane potential dynamics and spike pattern sequences (raster plots).
- The model exhibits generically periodic dynamics.
- A weak sensitivity to initial conditions was identified due to a sharp threshold mechanism.
Conclusions:
- The discrete time spiking neuron model displays a complex dynamical regime.
- This regime is numerically indistinguishable from chaos, despite underlying periodic dynamics.
- The findings contribute to understanding the emergence of complex behavior in simplified neural models.
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