FitzHugh-Nagumo model

i wish to solve the equations v'=v^3/3-w+i, w'=g(v+a-bw) with a=0.8, b=0.7, g=0.08, i=0.5 using ode45 in matlab. i solved in on paper but i don't know how to type the codes in matlab.

i googled this but for one unfamiliar with the code, it is hard to fathom what they are solving i also would like the code to show the plots of both variables changing with time and the phase plots of both variables.

Answer 1

[Alan Stevens]

Like so:

% Replace the following constants with your own values
tspan = [0 1];  % start and end times
v0 = 0; w0 = 0; % initial values
IC = [v0 w0];
% Call ode45
[t, vw] = ode45(@fn, tspan,IC);
% Extract individual solution values
v = vw(:,1);
w = vw(:,2);
% Plot results
plot(t,v,'r',t,w,'b'),grid
xlabel('t'),ylabel('v and w')
legend('v','w')

function dvwdt = fn(~,vw)
        
         a = 0.8; 
         b = 0.7;
         g = 0.08;
         i = 0.5;
         v = vw(1);
         w = vw(2);
         dvwdt = [v^3/3 - w + i;
                  g*(v+a-b*w)];          

end