Download Arc RDNR - Grenoble

Arc RDNR
Réseaux Dynamiques Non Réguliers
Participants :
Cortex, LORIA.
Bipop, INRIA Grenoble.
Mosaic, IMAG.
Financement :
Postdoc + Stages + missions
Nonsmooth dynamics
• Mechanic (impact, friction)
• Electrical systems (circuit)
• Biology (genetic, neuroscience)
Ideal charactetistic
Discontinuous dynamical systems.
(diode)
Numerical simulation
of spiking neural networks
• Time-stepping method
• Event-driven scheme
• State-stepping method
From Gerstner & Kistler
Compute accurately and efficiently spike times.
Neural code ?
STDP
Large scale neuronal
networks (106, 107)
Time-stepping schemes
t
Inactive neurons are updated !
Spike-spike corrections (smoothness on the PSP)
Event-driven schemes
where
Zero-crossing method (exact simulation)
Applied to a limited range of models
t
Event driven simulation of nonlinear integrate-and-fire neuron
(Neural Computation, 19:12, 2007)
1 – Formal integration
?
2 – Spike-test
Voltage stepping schemes
Nonlinear spike-generating current
• Based on a piecewise linear approximation of neuron dynamics.
We define a voltage-dependent linear integrate-and-fire neuron.
Time-stepping:
Voltage-stepping:
-Threshold event lies on an integration time-step boundary.
-Integration points are implicit and independent
(inactive neurons are not updated).
- The scheme is generic.
Voltage-stepping method
Voltage-stepping method
High activity regime
RK2 (log(E)=-6., N=50000)
Balanced regime
RK2 (log(E)=-3.6, N=25000)
Complementarity systems approach for spiking neural networks.
A theoretical framework
Efficient numerical schemes