P_bistability.m

%%%%%%%%%%%%%%%%%%%% (P) Bistability %%%%%%%%%%%%%%%%%%%%
% Some neurons can exhibit two stable modes of operation: resting and tonic
% spiking; an excitatory or inhibitory pulse can switch between the modes
% thereby creating an interesting possibility for bistability and
% short-term memory.

clear variables;

a=0.1;  b=0.26;  c=-60;  d=0;
j=0.04;  k=5;  l=140;
r=false;

u=-61;  % threshold value of the model neuron
w=b*u;

udot=[]; 
wdot=[];
grad_u=[]; 
grad_w=[];

tau = 0.25;
tspan = 0:tau:300;
T1=tspan(end)/8;
T2 = 216;

for t=tspan
    if ((t>T1) && (t < T1+5)) || ((t>T2) && (t < T2+5)) 
        I=1.24;
    else
        I=0.24;
    end
    
    [u, w, du, dw, ud, wd] = izhikevich(a, b, c, d, j, k, l, u, w, I, tau, r);
    udot(end+1)=ud;
    wdot(end+1)=wd;
    grad_u(end+1)=du;
    grad_w(end+1)=dw;
end

% plot membrane potential
fig = figure;
plot(tspan,udot,[0 T1 T1 (T1+5) (T1+5) T2 T2 (T2+5) (T2+5) max(tspan)],...
    -90+[0 0 10 10 0 0 10 10 0 0]);
axis([0 max(tspan) -90 30])
xlabel('time')
ylabel('membrane potential')
title('(P) bistability');
print(fig,'img/P_bistability_membrane_potential.png','-dpng')

% plot phase portrait
fig = figure;
hold on;
plot(udot,wdot)
quiver(udot,wdot,grad_u,grad_w,'r')
xlabel('membrane potential')
ylabel('recovery variable')
title('(P) bistability phase portrait');
print(fig,'img/P_bistability_phase_portrait.png','-dpng')