MATLAB ode45函数可以采用矢量数组值吗？

Question

I am getting an error in my code. The error is

" Error using odearguments ( line 93) @(T,IP)V4.*(C+(1-ALPHA).*K4)./(C+K4)-
(IR*IP) returns a vector of length 10000, but the length of initial 
conditions vector is 1. The vector returned by @(T,IP)V4.*(C+(1-
ALPHA).*K4)./(C+K4)-(IR*IP) and the initial conditions vector must 
have the same number of elements "

. The error is generated from the last ODE45 function.

This is the code :

clear all; clc;
%--------------------------------------------------------------------------
% The simulation is based on the model described by DeYoung and Keizer in 
% the paper titled " A single-pool inositol 1,4,5-trisphosphate-receptor-
% based model for agonist-stimulated oscillations in Ca2+ concentration"
%--------------------------------------------------------------------------
%--------------------------------------------------------------------------
% Initial conditions
%--------------------------------------------------------------------------
Ca_ER=10*10^-6;  Ca_cyto=1.7*10^-6;
Ir=1;  alpha=.5;  p_open3=0.15;
%--------------------------------------------------------------------------
% Constants in micromolar
%--------------------------------------------------------------------------
c0=4*10^-6;   c1=.185;  
v1=6;  v2=.11;  v3=.09*10^-6;  v4=1.2;  
k3=.1*10^-6;  k4=1.1*10^-6;
%--------------------------------------------------------------------------
% Receptor Binding Constants in micromolar per second
%--------------------------------------------------------------------------
a1=400*10^-6;  a2=0.2*10^-6;  a3=400*10^-6;  a4=0.2*10^-6;  a5=20*10^-6;
%--------------------------------------------------------------------------
% Receptor Dissociation Constants in micromolar 
%--------------------------------------------------------------------------
d1=0.13*10^-6;  d2=1.049*10^-6;  d3=.9434*10^-9;  d4=.1445*10^-9;  
d5=.08234*10^-9;
%--------------------------------------------------------------------------
% ODE describing Ca2+ concentrations in the cyctosol. Refer Ca2+
% oscillations
%--------------------------------------------------------------------------
dc=@(t,c) (c1.*(v1.*(p_open3)+v2).*(Ca_ER)-c)-v3.*((c).^2)./(c.^2+(k3).^2);
[t,c]=ode45(dc,linspace(0, 100, 10000),.15*10^-6);
plot(t,c);
%--------------------------------------------------------------------------
% Obtaining Ca_ER from the conservation condition. Refer Ca2+ oscillations
%--------------------------------------------------------------------------
Ca_ER=(c0-c)./c1;
figure(2);
plot(t,Ca_ER);
%--------------------------------------------------------------------------
%ODE describing IP3 production by Ca2+ feedback. Refer equation 4
%--------------------------------------------------------------------------
dIP3= @(t,ip) v4.*(c+(1-alpha).*k4)./(c+k4)-(Ir*ip);
[t,ip3]=ode45(dIP3,linspace(0, 100),.2*10^-6);
plot(t,ip3);`

Answer 1

You need to solve for both functions in the same time. Something like:

clear all; clc;


%// Constants - units look nice as comments :-D

Ca_ER   = 10e-6;
Ca_cyto = 1.7e-6;
Ir      = 1;
alpha   = 0.5;
p_open3 = 0.15;

c0 = 4e-6;
c1 = 0.185;  
v1 = 6;
v2 = 0.11;
v3 = 0.09e-6;
v4 = 1.2;  
k3 = 0.1e-6;
k4 = 1.1e-6;

a1 = 400e-6;
a2 = 0.2e-6;
a3 = 400e-6;
a4 = 0.2e-6;
a5 = 20e-6;

d1 = 0.13e-6;
d2 = 1.049e-6;
d3 = 0.9434e-9;
d4 = 0.1445e-9;  
d5 = 0.08234e-9;


%// Solving for f where:
%//  f(1) = Ca2+ conc
%//  f(2) = IP3

df = @(t,f) [                                                     ...
   c1*(v1*p_open3 + v2)*Ca_ER - f(1) - v3*f(1)^2/(f(1)^2 + k3^2); ...
   v4*(f(1)+k4*(1-alpha))/(f(1)+k4)  - Ir*f(2)                    ...
];
f0 = [      ...
   0.15e-6; ...
   0.2e-6   ...
];

[t,f] = ode45(df, linspace(0, 100, 10000), f0);


%// Separate solutions

c      = f(:,1);
ip3    = f(:,2);
Ca_ER1 =(c0-c)./c1;


%// Plots

figure(); plot(t, c);
figure(); plot(t, Ca_ER1);
figure(); plot(t, ip3);