function varargout = OneIzhikevichNetworkSimulator(varargin)
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @OneIzhikevichNetworkSimulator_OpeningFcn, ...
'gui_OutputFcn', @OneIzhikevichNetworkSimulator_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end
if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
function plotbutton_Callback(hObject, eventdata, handles)
global hfig_graphics
%% DECLARE PARAMETERS
%These are the indidivdual parameters for the Izhikevich Neuron
C = str2double(get(handles.C_,'string')); %Capacitance
vr = str2double(get(handles.vrest_,'string')); %Resting Membrane Potential
b = str2double(get(handles.b_,'string')); %Resonator/Integrator Variable
k = str2double(get(handles.k_,'string')); %Spike Width Factor
vpeak = str2double(get(handles.vpeak_,'string')); %Spike peak
Tsyn = str2double(get(handles.Tsyn_,'string')); %Synaptic time constant
Smax = str2double(get(handles.Smax_,'string')); %Jump in the conductance
c = str2double(get(handles.vreset_,'string')); %voltage reset
T = str2double(get(handles.T_,'string')); %Total simulation time
vt=vr+40-(b/k); %threshold
Er = 0; %Reversal Potential
%------------------------------------------------------------------
%------------Network Specific Parameters--------------------
I = str2double(get(handles.I_,'string')) ; %Applied Current
N = str2double(get(handles.N_,'string')); %Number of neurons
g = str2double(get(handles.g_,'string')); %maximal conductance
%This next command is used to initialize the mean adaptation variable
u = str2double(get(handles.uint_,'string'))*ones(N,1);
%This next comamnd is use to initialize the synaptic gating variables
S = str2double(get(handles.Sint_,'string'))*ones(N,1);
a = str2double(get(handles.a_,'string')); %reciprocal of adaptation decay time
d = str2double(get(handles.d_,'string')); %adaptation jump
%-----------Euler integration parameters ------------------
dt = 0.01; % Euler Integration Step;
%----------Other parameters
%-----Initialization---------------------------------------------
v = vr+(vpeak-vr)*rand(N,1); %initial distribution
v_ = v; %These are just used for Euler integration, previous time step storage
%---------Storage matrices --------------------------------------
vstore = zeros(T/dt,2); %store v
ustore = zeros(T/dt,2); %store u
sstore = zeros(T/dt,1); %store u
Neuron_Number1 = ceil(N*rand); % Pick neuron from the network to store data to
v(Neuron_Number1) = c; %initialize the neuron with the same membrane potential
handles.N = N;
in = zeros(N,1); %Initialize the spike firing index for network 1
tspike = zeros(N,120); %storage matix for spike time
DTspike = size(tspike);
%These equations can be manipulated if one wants to add sparsity to the
%network. SMAX is the connection matrix, and neff is the normalization
%constant.
SMAX = Smax*ones(N,N); neff = N;
%Store the initial conditions for the designated neurons
sstore(1,:) = [g*S(Neuron_Number1)];
vstore(1,:) = [v(Neuron_Number1),mean(v)]; %Store v
ustore(1,:) = [u(Neuron_Number1),mean(u)]; %Store u
%% SIMULATION
tic
for i = 0:T/dt;
%% EULER INTEGRATE
%This command is used to change the value of k so that the subthreshold and
%superthreshold response are different enough to get the right spike width.
% k = 5*(v>vt) + (v<vt)*0.15;
%-------------------Euler integration--------------------
v = v + dt*(( k.*(v-vr).*(v-vt) - u + I + g*(Er-v).*S)/C) ; % v(t) = v(t-1)+dt*v'(t-1)
u = u + dt*(a*(b*(v_-vr)-u)); %same with u, the v_ term makes it so that the integration of u uses v(t-1), instead of the updated v(t)
%--------------------------------------------------------
%-----Store spike times command ---------------------------------
logic = (v>=vpeak); %Figure out which neurons are firing
if sum(logic)>0
in = in + (logic); %Compute the total number of spikes fired
if max(in)>max(DTspike(2))
tspike(:,end+1:end+10) = zeros(N,10);
DTspike = size(tspike);
end
n = find(logic); %Find the neurons that specifically fired a spike
tspike(sub2ind(DTspike,n,in(n)))=dt*i;
end
%tspike(n,in(n)) = dt*i; %Store the time they fired it.
%------------------------------------------------------------------
%% COMPUTE S, APPLY RESETS
index = find((v>Er).*(v_<Er)); %this command finds the neurons in network 1 that have crossed the reversal potential
if isempty(index)==1 %If no spikes have fired, just implement the exponential decay in the conductances from network 1 to its postsynaptic connections
S = S+dt*(-S/Tsyn);
else
xs1 = SMAX(:,index)'; %This command draws only the columns of SMAX that are from the presynaptic firing neurons
j = size(index); %Compute the number of neurons that have simultaneously fired in this network
if j(1)>1, %If there are multiple neurons, we add the row sum to SIJ and implement exponential decay
S = S + dt*(-S/Tsyn)+ sum(xs1)'/neff;
else %If only one neuron fired, simply add the relevant column of SMAXIJ to SIJ, and implement exponential decay
S = S + dt*(-S/Tsyn) + xs1'/neff;
end
end
S = S + (1-S).*(S>1); %These commands bound each SIJ so that they cannot exceed 1.
u = u + d*(v>=vpeak); %implements set u to u+d if v>vpeak, component by component.
v = v+(c-v).*(v>=vpeak); %implements v = c if v>vpeak add 0 if false, add c-v if true, v+c-v = c
v_ = v; % sets v(t-1) = v for the next itteration of loop
vstore(i+1,:) = [v(Neuron_Number1),mean(v)]; %store v
ustore(i+1,:) = [u(Neuron_Number1),mean(u)]; %sotre u
sstore(i+1,:) = [g*S(Neuron_Number1)]; %store the conductances
end
toc
% PLOTTING AND STORAGE
handles.tspike = tspike;
%
%Plotting V
axes(hfig_graphics.vplot);
cla(hfig_graphics.vplot,'reset')
plot(0:dt:T,vstore), hold on %plotting v
plot(tspike(Neuron_Number1,:),vpeak + 0*tspike(Neuron_Number1,:),'*k')
ylabel('v')
% %Plotting U
axes(hfig_graphics.uplot);
cla(hfig_graphics.uplot,'reset')
plot(0:dt:T,ustore), hold on %plotting u
ylabel('u')
axes(hfig_graphics.splot);
cla(hfig_graphics.splot,'reset')
plot(0:dt:T,sstore(:,1)), hold on %plotting u
ylabel('g(t)')
%plot the mean voltage, adaptation, and conductance in a different figure
figure(100)
subplot(2,1,1)
plot(0:dt:T,ustore(:,2)), hold on %plotting u
ylabel('$\langle W(t)\rangle$','Interpreter','LaTeX','FontSize',14)
xlabel('Time (ms)','Interpreter','LaTeX','FontSize',14)
subplot(2,1,2)
plot(0:dt:T,sstore(:,1)), hold on %plotting u
ylabel('$g(t)$','Interpreter','LaTeX','FontSize',14)
xlabel('Time (ms)','Interpreter','LaTeX','FontSize',14)
guidata(hObject, handles);
function rasterplots_Callback(hObject, eventdata, handles)
figure(10)
%Plot the spike time raster plots for 25 neurons in a new figure
if handles.N>25; j = 25; else j = handles.N; end
for ner = 1:j
st = handles.tspike(ner,:);
st = st(st~=0);
plot(st,ner*ones,'k*'), hold on
end
xlabel('Time (ms)')
ylabel('Neuron Index')
guidata(hObject,handles)
% --- Executes on button press in QSSA.
function QSSA_Callback(hObject, eventdata, handles)
global hfig_graphics
C = str2double(get(handles.C_,'string')); %Capacitance
vr = str2double(get(handles.vrest_,'string')); %Resting Membrane Potential
b = str2double(get(handles.b_,'string')); %Resonator/Integrator Variable
k = str2double(get(handles.k_,'string')); %Spike Width Factor
vpeak = str2double(get(handles.vpeak_,'string')); %Spike peak
Tsyn = str2double(get(handles.Tsyn_,'string')); %Synaptic time constant
Smax = str2double(get(handles.Smax_,'string')); %Jump in the conductance
c = str2double(get(handles.vreset_,'string')); %voltage reset
T = str2double(get(handles.T_,'string')); %Total simulation time
vt=vr+40-(b/k); %threshold
Er = 0; %Reversal Potential
I = str2double(get(handles.I_,'string')) ; %Applied Curren
g = str2double(get(handles.g_,'string')); %synaptic conductance
a = str2double(get(handles.a_,'string')); %reciprocal of adaptation decay time
d = str2double(get(handles.d_,'string')); %adaptation jump
uint = str2double(get(handles.uint_,'string')); %initialize the mean adaptation and synaptic gating variable
sint = str2double(get(handles.Sint_,'string'));
%Dimensionless Parameters
alpha = 1+vt/abs(vr)
g = g/(k*abs(vr))
sint
wint = uint/(k*vr^2)
I = I/(k*vr^2)
er = 1+Er/abs(vr)
vpeak = 1 + vpeak/abs(vr)
vreset = 1 + c/abs(vr)
wjump = d/(k*vr^2)
sjump = Smax
T = T*k*abs(vr)/C
ts = Tsyn*k*abs(vr)/C
tw = (1/a)*(k*abs(vr))/C
%Simulate the mean field equations with the parameters from the GUI
%(Simulations are in dimensionless coordinates)
[t,y] = ode45(@(t,y) ONEIZNETWORKQSSA(alpha,g,I,er,vpeak,vreset,ts,tw,sjump,wjump,t,y)',[0,T],[sint,wint]');
%Plot dimensional adaptation variable (w/u)
axes(hfig_graphics.uplot);
plot(C*t/(k*abs(vr)),k*(vr^2)*y(:,2),'r','LineWidth',2), hold on %plotting u
ylabel('u')
%Plot dimensional conductance
axes(hfig_graphics.splot);
plot(C*t/(k*abs(vr)),k*abs(vr)*g*y(:,1),'r','LineWidth',2 ), hold on %plotting g
ylabel('g(t)')
%Plot all the variables of interest in a new figure.
figure(100)
subplot(2,1,1)
plot(C*t/(k*abs(vr)),k*(vr^2)*y(:,2),'r','LineWidth',2), hold on
ylabel('$W(t)$','Interpreter','LaTeX','FontSize',14)
xlabel('Time (ms)','Interpreter','LaTeX','FontSize',14)
subplot(2,1,2)
plot(C*t/(k*abs(vr)),k*abs(vr)*g*y(:,1),'r','LineWidth',2 ), hold on %plotting g
ylabel('$g(t)$','Interpreter','LaTeX','FontSize',14)
xlabel('Time (ms)','Interpreter','LaTeX','FontSize',14)
guidata(hObject,handles)
function CLEARPLOTS_Callback(hObject, eventdata, handles)
%this call back plots the average derivative of a_ neuron in the network
%Plotting V
global hfig_graphics
axes(hfig_graphics.vplot);
cla(hfig_graphics.vplot,'reset')
axes(hfig_graphics.uplot);
cla(hfig_graphics.uplot,'reset')
axes(hfig_graphics.splot);
cla(hfig_graphics.splot,'reset')
axes(hfig_graphics.rplot);
cla(hfig_graphics.rplot,'reset')
guidata(hObject,handles)
function OneIzhikevichNetworkSimulator_OpeningFcn(hObject, eventdata, handles, varargin)
plots;
global hfig_graphics
handles.output = hObject;
guidata(hObject, handles);
function rplot_Callback(hObject, eventdata, handles)
function globalu_Callback(hObject, eventdata, handles)
function alltoall_Callback(hObject, eventdata, handles)
function Tsyn__Callback(hObject, eventdata, handles)
function Tsyn__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function Smax__Callback(hObject, eventdata, handles)
function Smax__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function N__Callback(hObject, eventdata, handles)
function N__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function varargout = OneIzhikevichNetworkSimulator_OutputFcn(hObject, eventdata, handles)
plots
varargout{1} = handles.output;
function C__Callback(hObject, eventdata, handles)
function C__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function k__Callback(hObject, eventdata, handles)
function k__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function vreset__Callback(hObject, eventdata, handles)
function vreset__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function vpeak__Callback(hObject, eventdata, handles)
function vpeak__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function vrest__Callback(hObject, eventdata, handles)
function vrest__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function a__Callback(hObject, eventdata, handles)
function a__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function b__Callback(hObject, eventdata, handles)
function b__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function d__Callback(hObject, eventdata, handles)
function d__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function T__Callback(hObject, eventdata, handles)
function T__CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function rastplot_Callback(hObject, eventdata, handles)
function kde_Callback(hObject, eventdata, handles)
function qflux_Callback(hObject, eventdata, handles)
function pushbutton39_Callback(hObject, eventdata, handles)
function Sint__Callback(hObject, eventdata, handles)
function Sint__CreateFcn(hObject, eventdata, handles)
% hObject handle to Sint_ (see GCBO)
% eventdata reserved - to be defined in a_ future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a_ white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function uint__Callback(hObject, eventdata, handles)
function uint__CreateFcn(hObject, eventdata, handles)
% hObject handle to uint_ (see GCBO)
% eventdata reserved - to be defined in a_ future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a_ white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function g__Callback(hObject, eventdata, handles)
function g__CreateFcn(hObject, eventdata, handles)
% hObject handle to g_ (see GCBO)
% eventdata reserved - to be defined in a_ future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a_ white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function I__Callback(hObject, eventdata, handles)
function I__CreateFcn(hObject, eventdata, handles)
% hObject handle to I_ (see GCBO)
% eventdata reserved - to be defined in a_ future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a_ white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function a_Callback(hObject, eventdata, handles)
function a_CreateFcn(hObject, eventdata, handles)
% hObject handle to a_ (see GCBO)
% eventdata reserved - to be defined in a_ future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a_ white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function d_Callback(hObject, eventdata, handles)
function d_CreateFcn(hObject, eventdata, handles)
% hObject handle to d_ (see GCBO)
% eventdata reserved - to be defined in a_ future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a_ white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end