A question about FitzHugh-Nagumo model

Question

shuhao hu 2021-11-9

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1582139-a-question-about-fitzhugh-nagumo-model

评论： shuhao hu 2021-11-15

I`ve been trying to built the FitzHugh-Nagumo model with a changeable input,but I failed to make the input changeable and I was unable to figure out why.

I defined three variables which I thought they should be the same,but only the variable 'eq1' and the way I put in the comment worked out,the others ended without graph out.I wonder how could this happened and how should I change the code of 'eq2' and 'eq3' .

syms t

tspan = [0 100];

v0 = 0; w0 = 0;

IC = [v0 w0];

A=0.5;

B=0.05;

Epsilon=0.005;

I=sin(t);

eq1=@(t,vw)fn(t,vw,A,B,Epsilon,sin(t));

eq2=@(t,vw)fn(t,vw,A,B,Epsilon,0)+[sin(t);0];

eq3=@(t,vw)fn(t,vw,A,B,Epsilon,I);

[t, vw] = ode45(eq1, tspan,IC);

%[t, vw] = ode45(@(t,vw)fn(t,vw,A,B,Epsilon,sin(t)), tspan,IC);

v = vw(:,1);

w = vw(:,2);

% results

plot(t,v,'r',t,w,'b'),grid

xlabel('t'),ylabel('v and w')

legend('v','w')

function dvwdt = fn(~,vw,A,B,Epsilon,I)

a = A;

b = B;

epsilon = Epsilon;

i = I;

v = vw(1);

w = vw(2);

dvwdt = [(v*(v-a)*(1-v)-w+i)/epsilon;

v-w-b];

end

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Answer 1

Alan Stevens 2021-11-9

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在 MATLAB Online 中打开

Like this?

tspan = [0 100];

v0 = 0; w0 = 0;

IC = [v0 w0];

A=0.5;

B=0.05;

Epsilon=0.005;

I=@(t)sin(t); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

eq1=@(t,vw)fn(t,vw,A,B,Epsilon,sin(t));

eq2=@(t,vw)fn(t,vw,A,B,Epsilon,0)+[sin(t);0];

eq3=@(t,vw)fn(t,vw,A,B,Epsilon,I(t));

[t1, vw1] = ode45(eq1, tspan,IC);

[t2, vw2] = ode45(eq2, tspan,IC);

[t3, vw3] = ode45(eq3, tspan,IC);

v1 = vw1(:,1); v2 = vw2(:,1); v3 = vw3(:,1);

w1 = vw1(:,2); w2 = vw2(:,2); w3 = vw3(:,2);

% results

figure

plot(t1,v1,'r',t1,w1,'b'),grid

xlabel('t1'),ylabel('v1 and w1')

legend('v1','w1')

figure

plot(t2,v2,'r',t2,w2,'b'),grid

xlabel('t2'),ylabel('v2 and w2')

legend('v2','w2')

figure

plot(t3,v3,'r',t3,w3,'b'),grid

xlabel('t3'),ylabel('v3 and w3')

legend('v3','w3')

function dvwdt = fn(~,vw,A,B,Epsilon,I)

a = A;

b = B;

epsilon = Epsilon;

i = I;

v = vw(1);

w = vw(2);

dvwdt = [(v*(v-a)*(1-v)-w+i)/epsilon;

v-w-b];

end

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Alan Stevens 2021-11-12

In eq2, the value of I passed to fn is zero. To see the effect this has change eq2 so that it doesn't add the [sin(t); 0] term. You will then see that this last vector just produces oscillations about two very different values.

shuhao hu 2021-11-15