% This is a MATLAB code to generate Figure 3 of 
% Vocal development throught morphological computation
% Zhang YS, Ghazanfar AA (2018)
% YSZ 01/22/2018

% Plot Figure 3B
% integrator parameter
dt = 0.01;      % time increment
N = 3000;
% scale the time
dur = 8;
Fs = N/dur;
% CPG model parameter
b1 = 4; % coupling coef. 2->1
b2 = 0.01; % coupling coef. 1->2
c1 = [3.4 3.1 2.8]; % time constant for x1
c2 = 25; % time constant for x2

% initial conditions
x0 = [-0.1;0;-.1;0];

% parameter for pressure conversion
p0 = 1;
P = 0.1;

% ramping, discard the first 2s
prct = 0.25; 
dmin = dur*prct;
I = zeros(1,round(N*prct)); % input
I = [I linspace(0,1,N-round(N*prct))];
% ramping input parameter to x1
a1min = 0;
a1max = 0;
% ramping input parameter to x2
a2min = -1;
a2max = 1;
a1 = I*(a1max-a1min)+a1min;
a2 = I*(a2max-a2min)+a2min;
    
figure
set(gcf,'position',[-500,100,800,800])
% plot ramping input
subplot(411)
line([0 dur-dmin],[0 1])
set(gca,'XTick',[])
set(gca,'XTicklabel',[])
box off
set(gca,'Fontsize',16)
set(gca,'Linewidth',1)
ylabel('I (a.u.)')
axis tight

for i = 1:length(c1)

% solve ODE
x = coupled_cpg_solver(x0,a1,a2,b1,b2,c1(i),c2,N,dt);
x = x(:,round(N*prct)+1:end);

% convert to pressure
a = tansig((x(1,:)*p0))*P; 

% smooth factors
alpha = 0.16;
nwin = alpha*Fs/2+1;
gwin = gausswin(nwin,alpha);
gwin = gwin/sum(gwin);
w = conv(a,gwin,'same');


subplot(4,1,i+1)
% plot pressure when c1=2.8
plot((0:length(w)-1)/Fs,w,'k')
hold off
set(gca,'XTicklabel',[0 1 2 3 4 5 6])
box off
set(gca,'Fontsize',16)
ylabel('p (a.u.)')
set(gca,'Linewidth',1)
xlim([dmin dur])
if i==4
xlabel('Time (s)')
end
axis tight
end

set(subplot(4,1,1),'Position',[0.15,0.80,0.8,0.18])
set(subplot(4,1,2),'Position',[0.15,0.5883,0.8,0.18])
set(subplot(4,1,3),'Position',[0.15,0.3667,0.8,0.18])
set(subplot(4,1,4),'Position',[0.15,0.15,0.8,0.18])


%%
% Plot Figure E,G
% Increase N1 and N2 to plot Figure 3D
% proportion simulation
a1min = 0;
a1max = 0;
a2min = -1;
a2max = 1;
b1 = 4;
b2 = 0.015;
c1min = 2;
c1max = 3;
c2 = 25; 

N1 = 100;
N2 = 20;

I = linspace(0,1,N1);
a1 = linspace(a1min,a1max,N1);
a2 = linspace(a2min,a2max,N1);
c1 = linspace(c1min,c1max,N2);

N1 = length(I);
N2 = length(c1);
L = 2000;
dt = 0.01;
Fs = 3000/8;
f=Fs*(0:L/2)/L;

% initial condition
x0 = [-0.1;0;-.1;0];

% bifurcation creteria
bifur1 = NaN(N1,N2);
bifur2 = NaN(N1,N2);
parfor l = 1:N2
mat = zeros(N1,L,4);
mat1 = [];
mat2 = [];

for i = 1:N1
    for j = 1:L
        if j == 1
            pre = x0;
            for k = 1:500 % discard the first 500
                k1=dt*coupledcpg(pre,a1(i),a2(i),b1,b2,c1(l),c2); 
                k2=dt*coupledcpg(pre+k1/2,a1(i),a2(i),b1,b2,c1(l),c2); 
                k3=dt*coupledcpg(pre+k2/2,a1(i),a2(i),b1,b2,c1(l),c2); 
                k4=dt*coupledcpg(pre+k3,a1(i),a2(i),b1,b2,c1(l),c2); 
                nxt = pre + k1/6+k2/3+k3/3+k4/6;
                pre = nxt;
            end
        end
        k1=dt*coupledcpg(pre,a1(i),a2(i),b1,b2,c1(l),c2); 
        k2=dt*coupledcpg(pre+k1/2,a1(i),a2(i),b1,b2,c1(l),c2); 
        k3=dt*coupledcpg(pre+k2/2,a1(i),a2(i),b1,b2,c1(l),c2); 
        k4=dt*coupledcpg(pre+k3,a1(i),a2(i),b1,b2,c1(l),c2); 
        nxt = pre + k1/6+k2/3+k3/3+k4/6;
        mat(i,j,:) = nxt;
        pre = nxt;  
    end
    % get spectrum
    yy = fft(mat(i,:,1));
    P = abs(yy/L);
    P1 = P(1:L/2+1);
    P1(2:end-1)=2*P1(2:end-1);
    % get weighted mean of frequency
    [~,locs]=findpeaks(P1,'minpeakheight',prctile(P1,99.5));
    mat1 = [mat1 f(locs)*P1(locs)'/sum(P1(locs))];

    flg1 = find(f(locs)<=7);
    flg2 = find(f(locs)>7);
    % get the ratio of fast and slow oscillations
    if (~isempty(flg1))&&(~isempty(flg2))
        pp1 = max(P1(locs(flg1)));
        pp2 = max(P1(locs(flg2)));
        pratio = pp1/pp2;
    elseif (~isempty(flg1))&&(isempty(flg2))
        pp1 = max(P1(locs(flg1)));
        pratio = pp1/median(P1);
    elseif (isempty(flg1))&&(~isempty(flg2))
        pp2 = max(P1(locs(flg2)));
        pratio = median(P1)/pp2;
    else
        pratio = NaN;
    end
    mat2 = [mat2 10*log10(pratio)];
end

bifur1(:,l) = mat1';
bifur2(:,l) = mat2';
end


%%
xxx={I,c1};
bf1s = csaps(xxx,bifur1,0.9995,xxx);
bf2s = csaps(xxx,bifur2,0.9995,xxx);

bifur3 = ones(size(bifur1));
bifur3(bf1s<=4&bf2s>5)=0;  % very slow oscillations are contact calls
bifur3(bf2s<3|bf1s>6)=2; % very fast oscillations are twitters
bifur3 = fliplr(bifur3);

% to plot bifurcation diagram, increase N1 to 1000 and N2 to 200
% figure
% % bifurcation
% imagesc(bifur3')
% axis xy

p1 = zeros(1,N2);
p2 = zeros(1,N2);

for i = 1:N2
    p1(i) = length(find(bifur3(:,i)==2))/N1;
    p2(i) = length(find(bifur3(:,i)==1))/N1;
end
p0 = 1-p1-p2;
p1s = csaps(c1,p1,0.999,c1);
p2s = csaps(c1,p2,0.999,c1);
p0s = csaps(c1,p0,0.999,c1);

figure(11)
subplot(2,1,1)
plot(c1,p1,'o')
hold on
plot(c1,p1s)
plot(c1,p2,'o')
plot(c1,p2s)
hold off
xlabel('Time constant')
ylabel('Proportion')
box off
ylim([0 0.4])
title('trill and twitter')
subplot(2,1,2)
plot(c1,p0,'o')
hold on
plot(c1,p0s)
hold off
xlabel('Time constant')
ylabel('Proportion')
ylim([0.5 1])
box off
title('contact call')
%%
% ode integrator using RK-4
function x = coupled_cpg_solver(x0,a1s,a2s,b1,b2,c1,c2,N,dt)
    x = zeros(4,N);
    x(:,1) = x0;

    for i = 2:N
        a1 = a1s(i) ;
        a2 = a2s(i);
        yy = x(:,i-1);
        k1=dt*coupledcpg(yy,a1,a2,b1,b2,c1,c2); 
        k2=dt*coupledcpg(yy+k1/2,a1,a2,b1,b2,c1,c2); 
        k3=dt*coupledcpg(yy+k2/2,a1,a2,b1,b2,c1,c2); 
        k4=dt*coupledcpg(yy+k3,a1,a2,b1,b2,c1,c2); 
        x(:,i)=yy+k1/6+k2/3+k3/3+k4/6; 
    end
end

% odes
function r = coupledcpg(x,a1,a2,b1,b2,c1,c2)
    r1 = x(2);
    r2 = (a1 - x(1) + x(2)/c1 - x(1)^2*x(2)/c1 + b1*x(4))*c1^2;
    r3 = x(4);
    r4 = (a2 - x(3) + x(4)/c2 - x(3)^2*x(4)/c1 + b2*x(2))*c2^2;
    r = [r1;r2;r3;r4];
end