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wc_rate.m
223 lines (193 loc) · 6.48 KB
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wc_rate.m
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clear all
close all
tf=2000; dt=0.1; N=(tf/dt);
ttstart = 0.1;
ttstop = tf;
fi=0; ff=0; % [Hz]
k=15; r0=0.5;
b=1; x0=5;
% w=6.3; A = 2.35;
w=6; A=2.5;
r = -10:0.01:10;
planes=1;
Iinp=0.8; %osc input amp
transient = 1000; %ms
tf=2000+transient; dt=0.1; N=(tf/dt);
ttstart = 0.1;
ttstop = tf;
fi=1; ff=50; % [Hz]
df=1;
taur=1; taun=25;
Rinf1 = @(x) 1./(1+exp(-(x-x0)));
ainf = @(r) 1./(1+exp(-k*(r-r0)));
anull = @(r,A) -(-w*r - A + x0 + log(r./(1-r)))/b;
if(planes==1)
figure(1);
subplot(1,2,1)
plot(r,ainf(r),'g','LineWidth',2); hold on;
plot(r,anull(r,A),'r','LineWidth',2); hold on;
% plot(r,anull(r,A+Iinp),'r--','LineWidth',2); hold on;
% plot(r,anull(r,A-Iinp),'r--','LineWidth',2); hold on;
xlim([0,1]); ylim([0,1]);
set(gca,'xtick',[]);
ylabel('second-variable')
title('negative feedback')
set(gca, 'FontName', 'Helvetica','FontSize',20)
subplot(1,2,2)
plot(r,ainf(r),'g','LineWidth',2); hold on;
plot(r,anull(r,A),'r','LineWidth',2); hold on;
% plot(r,anull(r,A+Iinp),'r--','LineWidth',2); hold on;
% plot(r,anull(r,A-Iinp),'r--','LineWidth',2); hold on;
xlim([0,1]); ylim([0,1]);
set(gca,'xtick',[]); set(gca,'ytick',[])
title('positive feedback')
set(gca, 'FontName', 'Helvetica','FontSize',20)
end
acum1=[];
acum2=acum1; acum3=acum1; acum4=acum1;
for f = fi:df:ff
% f=0;
pks1=[]; pks2=[];
% for taun = 100:1:100
r1=zeros(1,N); r1(1)=0.4;
n1=zeros(1,N); n1(1)=0.5;
r2=zeros(1,N); r2(1)=0.4;
n2=zeros(1,N); n2(1)=0.5;
Input=zeros(1,N);
for i = 1:N-1
t = i*dt;
if (t<transient)
I=A;
else
I = A+Iinp*sin(2*pi*f*t*10^-3);
end
%a
r1(i+1) = r1(i) + dt*(-r1(i) + Rinf1(w*r1(i) - b*n1(i) + I))/taur;
n1(i+1) = n1(i) + dt*(-n1(i) + ainf(r1(i)))/taun;
r2(i+1) = r2(i) + dt*(-r2(i) + Rinf1(w*r2(i) - b*n2(i) + I))/taur;
n2(i+1) = n2(i) + dt*(-n2(i) + ainf(r2(i)))/taun;
Input(i) = I;
end
figure(1)
% subplot(2,2,1)
% plot(r1,n1,'-','Color',[0,1,1],'LineWidth',0.1)
% subplot(2,2,2)
% plot(r2,n2,'-','Color',[0,1,1],'LineWidth',0.1)
% subplot(2,2,3)
% plot(r3,n3,'-','Color',[0,1,1],'LineWidth',0.1)
% subplot(2,2,4)
% plot(r4,n4,'-','Color',[0,1,1],'LineWidth',0.1)
if(f==1)
figure(1)
subplot(1,2,1)
plot(r1(20000:end),n1(20000:end),'-','Color',[0,1,1],'LineWidth',0.1) %end/2
subplot(1,2,2)
plot(r2(20000:end),n1(20000:end),'-','Color',[0,1,1],'LineWidth',0.1)
figure(4);
subplot(1,2,1)
plot(dt:dt:dt*N,r1,'Color',[0,1,1],'LineWidth',1); hold on;
set(gca,'xtick',[]);
ylabel('r')
set(gca, 'FontName', 'Helvetica','FontSize',20)
subplot(1,2,2)
plot(dt:dt:dt*N,r2,'Color',[0,1,1],'LineWidth',1); hold on;
set(gca,'xtick',[]); set(gca,'ytick',[])
set(gca, 'FontName', 'Helvetica','FontSize',20)
set(gca, 'FontName', 'Helvetica','FontSize',20)
elseif(f==15)
figure(1)
subplot(1,2,1)
plot(r1(20000:end),n1(20000:end),'-','Color',[1,0,1],'LineWidth',0.1)
subplot(1,2,2)
plot(r2(20000:end),n1(20000:end),'-','Color',[1,0,1],'LineWidth',0.1)
figure(4);
subplot(1,2,1)
plot(dt:dt:dt*N,r1,'Color',[1,0,1],'LineWidth',1)
set(gca,'xtick',[]);
ylabel('r')
set(gca, 'FontName', 'Helvetica','FontSize',20)
subplot(1,2,2)
plot(dt:dt:dt*N,r2,'Color',[1,0,1],'LineWidth',1)
set(gca,'xtick',[]); set(gca,'ytick',[])
set(gca, 'FontName', 'Helvetica','FontSize',20)
xlabel('Time [ms]')
set(gca, 'FontName', 'Helvetica','FontSize',20)
elseif(f==50)
figure(1)
subplot(1,2,1)
plot(r1(20000:end),n1(20000:end),'-','Color',[0,0,1],'LineWidth',0.1)
subplot(1,2,2)
plot(r2(20000:end),n1(20000:end),'-','Color',[0,0,1],'LineWidth',0.1)
figure(4);
subplot(1,2,1)
plot(dt:dt:dt*N,r1,'Color',[0,0,1],'LineWidth',1)
set(gca,'xtick',[]);
ylabel('r')
set(gca, 'FontName', 'Helvetica','FontSize',20)
subplot(1,2,2)
plot(dt:dt:dt*N,r2,'Color',[0,0,1],'LineWidth',1)
set(gca,'xtick',[]); set(gca,'ytick',[])
set(gca, 'FontName', 'Helvetica','FontSize',20)
xlabel('Time [ms]')
set(gca, 'FontName', 'Helvetica','FontSize',20)
end
if(f==1)
figure(10)
subplot(1,3,1)
plot(dt:dt:tf-dt,Input(1:end-1),'Color',[0,1,1],'LineWidth',2);
title('Input frequency = 1Hz')
ylabel('Input')
xlabel('Time (ms)')
set(gca, 'FontName', 'Helvetica','FontSize',20)
xlim([0,tf])
elseif(f==15)
figure(10)
subplot(1,3,2)
plot(dt:dt:tf-dt,Input(1:end-1),'Color',[1,0,1],'LineWidth',2)
title('Input frequency = 15Hz')
xlabel('Time (ms)')
set(gca, 'FontName', 'Helvetica','FontSize',20)
xlim([0,tf])
elseif(f==50)
figure(10)
subplot(1,3,3)
plot(dt:dt:tf-dt,Input(1:end-1),'Color',[0,0,1],'LineWidth',2)
title('Input frequency = 50Hz')
xlabel('Time (ms)')
set(gca, 'FontName', 'Helvetica','FontSize',20)
xlim([0,tf])
end
pks1 = [pks1; length(findpeaks(r1))/2];
pks2 = [pks2; length(findpeaks(r2))/2];
acum1 = [acum1; max(r1(end/2:end)) - min(r1(end/2:end))];% sum(r1)];
acum2 = [acum2; max(r2(end/2:end)) - min(r2(end/2:end))];% sum(r2)];
end
% figure;
% subplot(2,1,1)
% plot(pks1)
% xlabel('\tau_a [ms]')
% ylabel('Frequency [Hz]')
% title('1')
% set(gca, 'FontName', 'Helvetica','FontSize',14)
% subplot(2,1,2)
% plot(pks2)
% xlabel('\tau_a [ms]')
% ylabel('Frequency [Hz]')
% title('4')
% set(gca, 'FontName', 'Helvetica','FontSize',14)
figure(3);
subplot(1,2,1)
plot(acum1,'k','LineWidth',2); hold on;
plot(1,acum1(1),'o','Color',[0,1,1],'MarkerFaceColor',[0,1,1])
plot(15,acum1(15),'o','Color',[1,0,1],'MarkerFaceColor',[1,0,1])
plot(50,acum1(50),'o','Color',[0,0,1],'MarkerFaceColor',[0,0,1])
ylabel('r_{\rm max} - r_{\rm min}')
xlabel('Input frequency (Hz)')
set(gca, 'FontName', 'Helvetica','FontSize',14)
subplot(1,2,2)
plot(acum2,'k','LineWidth',2); hold on;
plot(1,acum2(1),'o','Color',[0,1,1],'MarkerFaceColor',[0,1,1])
plot(15,acum2(15),'o','Color',[1,0,1],'MarkerFaceColor',[1,0,1])
plot(50,acum2(50),'o','Color',[0,0,1],'MarkerFaceColor',[0,0,1])
xlabel('Input frequency (Hz)')
set(gca, 'FontName', 'Helvetica','FontSize',14)