MATLAB: How to enter in matlab syntax two parameters which are not exist in the system of nonlinear ode

MATLABnonlinear

Question: Ommega and Sigma are not in the system of equation. How can I enter matlab syntax or code including Ommega and Sigma using ode45?

dx(1)dt = alpha1*x(1)-alpha1*x(1).^2./kappa1-beta1*x(1)*x(2)-epsilon*gamma*x(1);

dx(2)dt = alpha2*x(2)-alpha2*x(2).^2./kappa2-beta2*x(1)*x(2)-gamma*x(2);

Best Answer

I think you may be asking how to parametise your odes.

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MATLAB: Coupled ODE with ode45

I found the mistake. It was a sign. :) The correct function is

function dz = myode(v,z)
alpha = 0.001;
C0 = 0.3;
esp = 2;
k = 0.044;
f0 = 2.5;
dz = zeros(2,1);
dz(1) = k*C0/f0*(1-z(1)).*z(2)./(1+esp*z(1));
dz(2) = -alpha*(1+esp*z(1))./(2*z(2));

MATLAB: Solving two systems of DEs using the ode45 function.

Vassil, check out

 function my_ode()
 alpha0 = 1;
 alpha1 = 1;
 beta0  = 1;
 beta1  = 1;
 lambda = 1;
 sigma  = 1;
 param  = [alpha0; alpha1; beta0; beta1; lambda; sigma];
 [t,X] = ode45(@EOM,[0 5],[1 2 3 4 5 6],[],param);
 plot(t,X(:,1))
 grid
 end
 function dX = EOM(t,x,param)
 x1     = x(1);
 x2     = x(2);
 x3     = x(3);
 alpha0 = param(1);
 alpha1 = param(2);
 beta0  = param(3);
 beta1  = param(4);
 lambda = param(5);
 sigma  = param(6);
 alpha  = alpha0+alpha1*t;
 beta   = beta0+beta1*t;
 dx1 = -2*lambda*beta*x1+2*lambda*alpha*x2+lambda^2*sigma^2;
 dx2 = beta*x1-(alpha+lambda*beta)*x2+lambda*alpha*x3;
 dx3 = 2*beta*x2-2*alpha*x3;
 dX1 = beta*x1;
 dX2 = alpha*x2;
 dX3 = x3;
 dX  = [dx1; dx2; dx3; dX1; dX2; dX3];
 end

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Related Solutions

MATLAB: Coupled ODE with ode45

MATLAB: Solving two systems of DEs using the ode45 function.

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