ODE error and vector error

Error in my code:

Error using odearguments (line 95)

@(T,X)BADSTROMARUN(T,X,A,A1,A2,B,B1,B2,B3,C1,C2,D1,D2) returns a vector of length 2, but the length of initial conditions

vector is 4. The vector returned by @(T,X)BADSTROMARUN(T,X,A,A1,A2,B,B1,B2,B3,C1,C2,D1,D2) and the initial conditions vector

must have the same number of elements.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in badstroma (line 37)

[t, x] = ode45(@(t,x)badstromarun(t,x,a,a1,a2,b,b1,b2,b3,c1,c2,d1,d2),tspan,X0);

Unsure what this means but I have tried multiple different ways to try and code my plots of cell growth

clc;

close all;

%define parameters

%x is the number of cancer cells

C0 = 100;

% c2 is the number of bad stromal cells

S0 = 100;

s1=C0/(C0+S0);

s2=S0/(C0+S0);

X0=[C0;S0;s1;s2];

% a, b is the growth rate of cancer cells

a = 0.35;

b = 0.35;

% a1 a2 growth rate of cancerous stroma

a1 = 0.01; %intrinsic growth

a2 = 0.01; %growth due to stroma

b1 = 0.1; % influence of bad stroma delay

b2 = 0.1; %stroma inheremnt prolifiration

b3 = 0.01; % strome slow-down prolifiration rate due to large number of stroma cells

c1=0.001; % dies naturally and due to C/S factor

d1=0.05; % natural death of stromA

c2=0.2; % dies due to stravation

d2=0.2; % dies due to stravation

%time parameter (measured in weeks)

t0=0; %initital time

t1=520; %final time

tspan=[t0 t1];

% plot result

[t, x] = ode45(@(t,x)badstromarun(t,x,a,a1,a2,b,b1,b2,b3,c1,c2,d1,d2),tspan,X0);

figure(1)

plot(t,real(x(:,1)))

figure(2)

plot(t,real(x(:,2)))

function xdot= badstromarun(~,x,a,a1,a2,b,b1,b2,b3,c1,c2,d1,d2)

xdot = zeros(2,1);

%xdot(1) = (a1+a2*(x(2)/(b1+x(2))))*x(1)*(1-log(x(1))/a)-x(1)*(c1*exp(x(1)/x(2))+c2*(1-s1));

%xdot(1) = (a1+a2*(x(2)/(b1+x(2)))-(c1*(exp(x(1)/x(2))-exp(1.0))+c2*(x(3))))*x(1)*(1-log(x(1))/a);

xdot(2) = (b2-b3*(exp(x(2)/x(1))-exp(1.0))-(d1+d2*(x(4))))*x(2)*(1-log(x(2))/b);

xdot(1) = (a1+a2*(x(1)/(b1+x(1))))*x(1)*(1-log(x(1))/a)-x(1)*(c1*exp(x(1)/x(2))+c2*(1-x(2)));

%xdot(2) = (b1-b1*0.01*exp(x(2)/x(1)))*x(2)*(1-log(x(2))/b)-x(2)*(d1+d2*(1-x(4)));

Any help would be greatly appreciated!

Answer 1

[Steven Lord]

As the error message states, your initial condition vector

X0=[C0;S0;s1;s2];

tells ode45 that you're trying to solve a system of four ODEs. However your ODE function

function xdot= badstromarun(~,x,a,a1,a2,b,b1,b2,b3,c1,c2,d1,d2)
 
xdot = zeros(2,1);

only returns values for two of the four ODEs. This mismatch causes MATLAB to throw the error.

If you have a system of four ODEs (or perhaps two second-order ODEs, in which case your system looks like the van der Pol equation example on this documentation page except with another pair of first-order ODEs constructed from your second second-order ODE) modify badstromarun so it returns a 4-by-1 vector with the values of each of the four ODEs.

If you have a system of two ODEs, change your X0 vector so it only has two elements.