Bound an odeint variable

Question

I\'m using odeint to simulate a system wherein there are several variables which should not go less than zero.

Is there an appropriate way to bound a variable in ode

Answer 1

What you need is sometimes called a "saturation" constraint, a common issue in dynamic systems modeling. You can easily code it inside your equation:

void YourEquation::operator() (const state_type &x, state_type &dxdt, const time_type t)
{
    // suppose that x[0] is the variable that should always be greater/equal 0
    double x0 = x[0]; // or whatever data type you use
    dxdt[0] = .... // part of your equation here
    if (x0 <= 0 && dxdt[0] < 0)
    {
        x0 = 0;
        dxdt[0] = 0
    }
    // the rest of the system equations, use x0 instead of x[0] if necessary, actually it depends on the situation and physical interpretation
    dxdt[1] = ....
    dxdt[2] = ....
    ...
}