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187 changes: 95 additions & 92 deletions
187
src/test/resources/codegeneration/aeif_cond_alpha.nestml
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| Original file line number | Diff line number | Diff line change |
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| /* | ||
| Name: aeif_cond_alpha - Conductance based exponential integrate-and-fire neuron | ||
| model according to Brette and Gerstner (2005). | ||
| Name: iaf_psc_alpha - Leaky integrate-and-fire neuron model. | ||
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| Description: | ||
| aeif_cond_alpha is the adaptive exponential integrate and fire neuron according | ||
| to Brette and Gerstner (2005). | ||
| Synaptic conductances are modelled as alpha-functions. | ||
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| This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with | ||
| adaptive step size to integrate the differential equation. | ||
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| The membrane potential is given by the following differential equation: | ||
| C dV/dt= -g_L(V-E_L)+g_L*Delta_T*exp((V-V_T)/Delta_T)-g_e(t)(V-E_e) | ||
| -g_i(t)(V-E_i)-w +I_e | ||
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| and | ||
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| tau_w * dw/dt= a(V-E_L) -W | ||
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| Integration parameters | ||
| gsl_error_tol double - This parameter controls the admissible error of the | ||
| GSL integrator. Reduce it if NEST complains about | ||
| numerical instabilities. | ||
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| Author: Marc-Oliver Gewaltig | ||
| iaf_psc_alpha is an implementation of a leaky integrate-and-fire model | ||
| with alpha-function shaped synaptic currents. Thus, synaptic currents | ||
| and the resulting post-synaptic potentials have a finite rise time. | ||
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| The threshold crossing is followed by an absolute refractory period | ||
| during which the membrane potential is clamped to the resting potential. | ||
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| The linear subthresold dynamics is integrated by the Exact | ||
| Integration scheme [1]. The neuron dynamics is solved on the time | ||
| grid given by the computation step size. Incoming as well as emitted | ||
| spikes are forced to that grid. | ||
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| An additional state variable and the corresponding differential | ||
| equation represents a piecewise constant external current. | ||
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| The general framework for the consistent formulation of systems with | ||
| neuron like dynamics interacting by point events is described in | ||
| [1]. A flow chart can be found in [2]. | ||
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| Critical tests for the formulation of the neuron model are the | ||
| comparisons of simulation results for different computation step | ||
| sizes. sli/testsuite/nest contains a number of such tests. | ||
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| The iaf_psc_alpha is the standard model used to check the consistency | ||
| of the nest simulation kernel because it is at the same time complex | ||
| enough to exhibit non-trivial dynamics and simple enough compute | ||
| relevant measures analytically. | ||
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| Remarks: | ||
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| The present implementation uses individual variables for the | ||
| components of the state vector and the non-zero matrix elements of | ||
| the propagator. Because the propagator is a lower triangular matrix | ||
| no full matrix multiplication needs to be carried out and the | ||
| computation can be done "in place" i.e. no temporary state vector | ||
| object is required. | ||
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| The template support of recent C++ compilers enables a more succinct | ||
| formulation without loss of runtime performance already at minimal | ||
| optimization levels. A future version of iaf_psc_alpha will probably | ||
| address the problem of efficient usage of appropriate vector and | ||
| matrix objects. | ||
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| Remarks: | ||
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| If tau_m is very close to tau_syn_ex or tau_syn_in, the model | ||
| will numerically behave as if tau_m is equal to tau_syn_ex or | ||
| tau_syn_in, respectively, to avoid numerical instabilities. | ||
| For details, please see IAF_Neruons_Singularity.ipynb in | ||
| the NEST source code (docs/model_details). | ||
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| References: | ||
| [1] Rotter S & Diesmann M (1999) Exact simulation of time-invariant linear | ||
| systems with applications to neuronal modeling. Biologial Cybernetics | ||
| 81:381-402. | ||
| [2] Diesmann M, Gewaltig M-O, Rotter S, & Aertsen A (2001) State space | ||
| analysis of synchronous spiking in cortical neural networks. | ||
| Neurocomputing 38-40:565-571. | ||
| [3] Morrison A, Straube S, Plesser H E, & Diesmann M (2006) Exact subthreshold | ||
| integration with continuous spike times in discrete time neural network | ||
| simulations. Neural Computation, in press | ||
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| Sends: SpikeEvent | ||
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| Receives: SpikeEvent, CurrentEvent, DataLoggingRequest | ||
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| References: Brette R and Gerstner W (2005) Adaptive Exponential | ||
| Integrate-and-Fire Model as an Effective Description of Neuronal | ||
| Activity. J Neurophysiol 94:3637-3642 | ||
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| SeeAlso: iaf_cond_alpha, aeif_cond_exp | ||
| FirstVersion: September 1999 | ||
| Author: Diesmann, Gewaltig | ||
| SeeAlso: iaf_psc_delta, iaf_psc_exp, iaf_cond_exp | ||
| */ | ||
| neuron aeif_cond_alpha_neuron: | ||
| neuron iaf_psc_alpha_neuron: | ||
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| state: | ||
| V_m mV = E_L # Membrane potential | ||
| w pA = 0 # Spike-adaptation current | ||
| V_abs mV | ||
| alias V_m mV = V_abs + E_L # Membrane potential. | ||
| end | ||
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| equations: | ||
| shape g_in = (e/tau_syn_in) * t * exp(-1/tau_syn_in*t) # Excitatory synaptic conductance in nS | ||
| shape g_ex = (e/tau_syn_ex) * t * exp(-1/tau_syn_ex*t) # Inhibitory synaptic conductance in nS | ||
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| # Add aliases to simplify the equation definition of V_m | ||
| exp_arg real = (V_m-V_th)/delta_T | ||
| I_spike pA = delta_T*exp(exp_arg) | ||
| I_syn_exc pA = Cond_sum(g_ex, spikesExc) * ( V_m - E_ex ) | ||
| I_syn_inh pA = Cond_sum(g_in, spikesInh) * ( V_m - E_in ) | ||
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| V_m' = ( -g_L * ( ( V_m - E_L ) - I_spike ) - I_syn_exc - I_syn_inh - w + I_e + I_stim ) / C_m | ||
| equations: | ||
| shape I_shape_in = (e/tau_syn_in) * t * exp(-1/tau_syn_in*t) | ||
| shape I_shape_ex = (e/tau_syn_ex) * t * exp(-1/tau_syn_ex*t) | ||
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| w' = (a*(V_m - E_L) - w)/tau_w | ||
| V_abs' = -1/Tau * V_abs + 1/C_m * (I_sum(I_shape_in, in_spikes) + I_sum(I_shape_ex, ex_spikes) + I_e + currents) | ||
| end | ||
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| parameter: | ||
| # membrane parameters | ||
| C_m pF = 281.0pF # Membrane Capacitance in pF | ||
| t_ref ms = 0.0ms # Refractory period in ms | ||
| V_reset mV = -60.0mV # Reset Potential in mV | ||
| g_L nS = 30.0nS # Leak Conductance in nS | ||
| E_L mV = -70.6mV # Leak reversal Potential (aka resting potential) in mV | ||
| I_e pA = 0pA # Constant Current in pA | ||
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| # spike adaptation parameters | ||
| a nS = 4nS # Subthreshold adaptation | ||
| b pA = 80.5pA # pike-triggered adaptation | ||
| delta_T mV = 2.0mV # Slope factor | ||
| tau_w ms = 144.0ms # Adaptation time constant | ||
| V_th mV = -50.4mV # Threshold Potential in mV | ||
| V_peak mV = 0mV # Spike detection threshold | ||
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| # synaptic parameters | ||
| E_ex mV = 0mV # Excitatory reversal Potential in mV | ||
| tau_syn_ex ms = 0.2ms # Synaptic Time Constant Excitatory Synapse in ms | ||
| E_in mV = -85.0mV # Inhibitory reversal Potential in mV | ||
| tau_syn_in ms = 2.0ms # Synaptic Time Constant for Inhibitory Synapse in ms | ||
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| # Input current injected by CurrentEvent. | ||
| # This variable is used to transport the current applied into the | ||
| # _dynamics function computing the derivative of the state vector. | ||
| I_stim pA = 0pA | ||
| C_m pF = 250pF # Capacity of the membrane | ||
| Tau ms = 10ms # Membrane time constant. | ||
| tau_syn_in ms = 2ms # Time constant of synaptic current. | ||
| tau_syn_ex ms = 2ms # Time constant of synaptic current. | ||
| t_ref ms = 2ms # Duration of refractory period in ms. | ||
| E_L mV = -70mV # Resting potential. | ||
| alias V_reset mV = -70mV - E_L # Reset potential of the membrane in mV. | ||
| alias Theta mV = -55mV - E_L # Spike threshold in mV. | ||
| I_e pA = 0pA # Constant external input current in pA. | ||
| end | ||
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| internal: | ||
| # Impulse to add to DG_EXC on spike arrival to evoke unit-amplitude | ||
| # conductance excursion. | ||
| PSConInit_E real = 1.0 * e / tau_syn_ex | ||
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| # Impulse to add to DG_INH on spike arrival to evoke unit-amplitude | ||
| # conductance excursion. | ||
| PSConInit_I real = 1.0 * e / tau_syn_in | ||
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| # refractory time in steps | ||
| RefractoryCounts integer = steps(t_ref) | ||
| # counts number of tick during the refractory period | ||
| r integer | ||
| RefractoryCounts integer = steps(t_ref) # refractory time in steps | ||
| r integer # counts number of tick during the refractory period | ||
| end | ||
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| input: | ||
| spikesInh <- inhibitory spike | ||
| spikesExc <- excitatory spike | ||
| currents <- current | ||
| ex_spikes <- excitatory spike | ||
| in_spikes <- inhibitory spike | ||
| currents <- current | ||
| end | ||
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| output: spike | ||
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| update: | ||
| integrate(V_m) | ||
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| if r > 0: # refractory | ||
| if r == 0: # neuron not refractory | ||
| integrate(V_abs) | ||
| else: # neuron is absolute refractory | ||
| r = r - 1 | ||
| end | ||
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| if r > 0: # not refractory | ||
| V_m = V_reset # clamp potential | ||
| elif V_m >= V_peak: | ||
| if V_abs >= Theta: # threshold crossing | ||
| # A supra-threshold membrane potential should never be observable. | ||
| # The reset at the time of threshold crossing enables accurate | ||
| # integration independent of the computation step size, see [2,3] for | ||
| # details. | ||
| r = RefractoryCounts | ||
| V_m = V_reset # clamp potential | ||
| w += b | ||
| V_abs = V_reset | ||
| emit_spike() | ||
| end | ||
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| # Update with initial values must be added after the model analysis | ||
| I_stim = currents.get_sum() | ||
| end | ||
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| end |
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