作者bankwn (duban)
看板MATLAB
标题[问题]fitzhugh-nagumo 模型 以I为参数的绘图
时间Fri Jul 5 02:17:29 2013
大家好 最近再重做前人的模拟 遇到苦思不解的麻烦
fitzhugh-nagumo 模型 (神经元活动的数学模型)
想要画出 I(x轴)-V(y轴) 大部分的文章都是 t-V图
最後找到几乎接近的 code 还是改不出来 XD
希望板上的大大们能指引1下 小弟程式不太行 :(
我想要模拟的 fitzhugh-nagumo 模型 I(电流)=0.05+(0.0005*t)^p p=1 or 2 or
0.5
(steven baer 2008的文章 Slow acceleration and deacceleration through a Hopf
bifurcation: Power ramps,
target nucleation, and elliptic bursting. 中的 fig 1& 2) 画出其 I-V图.
几乎可行的code (参数已改为要模拟的)
global I; % Need this so that function "f" knows about variable I
for I = [0.05:0.001:1]; % Loop over different values of applied current I
f = @(t,y) [-y(1)*(y(1)-0.2)*(y(1)-1)- y(2) + I; 0.05*(y(1) -0.4*y(2)) ];
g = @(y) f(0,y);
fp = fsolve(g,[0 0]); % Find the fixed point
Vss = fp(1); Wss = fp(2); % Get the steady-state V and W values from "fp"
hold on;
[T Y] = ode45(f, [0 100], Y(length(T),:) ); % Run some more in order
[T Y] = ode45(f, [0 100], Y(length(T),:) ); % to settle at equilibrium
plot(I, min(Y(:,1)), 'm.'); % minimum of V(t): a magenta point
plot(I, max(Y(:,1)), 'm.'); % maximum of V(t): a magenta point
plot(I,Vss,'.','color',color); % Fixed point: a red or blue point
title('Bifurcation diagram (V_{min}, V_{max}, V*)', 'fontsize', 12);
xlabel('I'); ylabel('V equilibrium');
axis tight;
drawnow;
end;
因为试过回圈 改I=y(3) 副程式等方式还是试不出来 希望有大大能帮忙 感谢 :)
能完整执行的code 在连结中 我的列子 要先执行过原档 (我只抓右下角的IT图)
http://web.njit.edu/~matveev/UBM/matlab.html 的 FN_Hopf.m
(Matlab code for the Fitzhugh-Nagumo model, showing the solution with initial
condition close to the fixed point, as the applied current I is varied.
Subthreshold Hopf bifurcation arises as the fixed point loses stability and
gives way to periodic spiking solution.)
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