%% SIMPLE SOLUTON FOR CPG MODEL
% The following parameters are described in 
% Yakovenko (2011) PBR PMID: 21333808
 
v = .1:.1:2.5;
u = (v+0.1272)/0.2357; % from Yakovenko, 2011
Tc = 0.5445*v.^(-0.5925); % from Halbertsma, 1983

% INTEGRATOR OFFETS
x01 = -0.0007;
x02 = 2.4256;

% INPUT PARAMETERS
gu1 = 0.6203;
gu2 = 0.4882;

% AUTOGENIC LEAK OF STATE
r11 = -0.0094;
r22 = r11;

% INITIAL CONDITIONS
x1 = -1;
x2 = 0;
x3 = -.5;
x4 = .5;

% The relationship derrived in Yakovenko, Sobinov, Gritsenko (2018):
Tc_sim = (x01+x02+(gu1+gu2)*u)./((x01+gu1*u).*(x02+gu2*u));

figure
subplot(1,3,1)
plot(v,Tc)
hold on 
plot(v,Tc_sim,'r')
ylim([0 2.5])
xlim([0 2.5])
axis square

subplot(1,3,2)
hold on
plot([0 2.5],[0 2.5],'k')
plot(Tc,Tc_sim,'r.')
axis square
ylim([0 2.5])
xlim([0 2.5])
[R,P] = corrcoef(Tc,Tc_sim);

subplot(1,3,3)
hold on
plot([0 2.5],[0 2.5],'k')
plot(v,u,'r.')
xlim([0 2.5])

axis square