# Error while solving a coupled system of ODE

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F.O on 17 Nov 2019
Commented: Star Strider on 17 Nov 2019
I am trying to solve a system of 6 coupled ODE my function works but I dont know why calling ode45 doesnt work.
My function is:
function [dxdt] = DM_bacteria(t,x,sigma,r,f,s,epsilon,omega,gamma12,g12)
dxdt(4)=x(4)*(r(4)*(1-(sigma(4,4)*x(4)+sigma(4,1)*x(1)+sigma(4,2)*x(2)+sigma(4,3)*x(3))/r(4))-f(4,1)*x(5)-f(4,2)*x(6))+s(4)
dxdt(5)=x(5)*(-epsilon(1)*(1+(omega(1,1)*x(5)+omega(1,2)*x(6))/epsilon(1))-g12*x(5)+beta(1,1)*f(1,1)*x(1)+beta(2,1)*f(2,1)*x(2)+beta(3,1)*f(3,1)*x(3)+beta(4,1)*f(4,1)*x(4))
dxdt(6)=x(6)*(-epsilon(2)*(1+(omega(2,2)*x(6)+omega(2,1)*x(5))/epsilon(2))-gamma12*g12*x(5)+beta(1,2)*f(1,2)*x(1)+beta(2,2)*beta(2,1)*f(2,2)*x(2)+beta(3,2)*f(3,2)*x(3)+beta(4,2)*f(4,2)*x(4))
dxdt(1)=x(1)*(r(1)*(1-(sigma(1,1)*x(1)+sigma(1,2)*x(2)+sigma(1,3)*x(3)+sigma(1,4)*x(4))/r(1))-f(1,1)*x(5)-f(1,2)*x(6))+s(1)
dxdt(2)=x(2)*(r(2)*(1-(sigma(2,2)*x(2)+sigma(2,1)*x(1)+sigma(2,3)*x(3)+sigma(2,4)*x(4))/r(2))-f(2,1)*x(5)-f(2,2)*x(6))+s(2)
dxdt(3)=x(3)*(r(3)*(1-(sigma(3,3)*x(3)+sigma(3,1)*x(1)+sigma(3,2)*x(2)+sigma(3,4)*x(4))/r(3))-f(3,1)*x(5)-f(3,2)*x(6))+s(3)
end
The script :
sigma=ones(4,4)
f=ones(4,2)
g12=1
gamma12=2
beta=ones(4,2)
omega=ones(2,2)
epsilon=[4,2]
s=[0 0 0 0]
x0=[600 600 600 600 600 600]
t = [0 20];
r=[1 2 3 4]
t=linspace(0,20,1000)
[dxdt] = DM_bacteria(t,x0,sigma,r,f,s,epsilon,omega,gamma12,g12)
[t,x]=ode45(@DM_bacteria,t,x0)
I got error :(I have all the argument in the function)!!
Not enough input arguments.
Error in DM_bacteria (line 3)
dxdt(4)=x(4)*(r(4)*(1-(sigma(4,4)*x(4)+sigma(4,1)*x(1)+sigma(4,2)*x(2)+sigma(4,3)*x(3))/r(4))-f(4,1)*x(5)-f(4,2)*x(6))+s(4)
Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.
Error in ode45 (line 115)
odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
Error in DynamicalModelBactera (line 14)
[t,x]=ode45(@DM_bacteria,t,x0)

Star Strider on 17 Nov 2019
Your ‘DM_bacteria’ function must return a column vector output.
This worked when I ran it just now:
function [dxdt] = DM_bacteria(t,x,sigma,r,f,s,epsilon,omega,gamma12,g12)
dxdt(4,:)=x(4)*(r(4)*(1-(sigma(4,4)*x(4)+sigma(4,1)*x(1)+sigma(4,2)*x(2)+sigma(4,3)*x(3))/r(4))-f(4,1)*x(5)-f(4,2)*x(6))+s(4);
dxdt(5,:)=x(5)*(-epsilon(1)*(1+(omega(1,1)*x(5)+omega(1,2)*x(6))/epsilon(1))-g12*x(5)+beta(1,1)*f(1,1)*x(1)+beta(2,1)*f(2,1)*x(2)+beta(3,1)*f(3,1)*x(3)+beta(4,1)*f(4,1)*x(4));
dxdt(6,:)=x(6)*(-epsilon(2)*(1+(omega(2,2)*x(6)+omega(2,1)*x(5))/epsilon(2))-gamma12*g12*x(5)+beta(1,2)*f(1,2)*x(1)+beta(2,2)*beta(2,1)*f(2,2)*x(2)+beta(3,2)*f(3,2)*x(3)+beta(4,2)*f(4,2)*x(4)) ;
dxdt(1,:)=x(1)*(r(1)*(1-(sigma(1,1)*x(1)+sigma(1,2)*x(2)+sigma(1,3)*x(3)+sigma(1,4)*x(4))/r(1))-f(1,1)*x(5)-f(1,2)*x(6))+s(1);
dxdt(2,:)=x(2)*(r(2)*(1-(sigma(2,2)*x(2)+sigma(2,1)*x(1)+sigma(2,3)*x(3)+sigma(2,4)*x(4))/r(2))-f(2,1)*x(5)-f(2,2)*x(6))+s(2);
dxdt(3,:)=x(3)*(r(3)*(1-(sigma(3,3)*x(3)+sigma(3,1)*x(1)+sigma(3,2)*x(2)+sigma(3,4)*x(4))/r(3))-f(3,1)*x(5)-f(3,2)*x(6))+s(3);
end
sigma=ones(4,4);
f=ones(4,2);
g12=1;
gamma12=2;
beta=ones(4,2);
omega=ones(2,2);
epsilon=[4,2];
s=[0 0 0 0];
x0=[600 600 600 600 600 600];
t = [0 20];
r=[1 2 3 4];
t=linspace(0,20,1000);
% [dxdt] = DM_bacteria(t,x0,sigma,r,f,s,epsilon,omega,gamma12,g12)
[t,x]=ode45(@(t,x)DM_bacteria(t,x,sigma,r,f,s,epsilon,omega,gamma12,g12),t,x0);
figure
plot(t, x)
grid
ylim([-10, 10])
Experiment to get different results.

F.O on 17 Nov 2019
Should I use ode45 or ode15s here ?
Star Strider on 17 Nov 2019
Your system does not appear to be ‘stiff’, and ode45 had no problems with it. I would just continue with ode45, unless the parameters change significantly in their relative magnitudes and the system becomes ‘stiff’.

R2019b

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