in the modelica language I found the time derivative of x used in this equation:
der(x) = 1 - x
as always the x is set to 0 by default, what I don't understand is how this equation drives the value of x towards 1.0.
reached the 2 seconds mark, shouldn't it go to negative instead of stabilizing to 1.0?
source: https://mbe.modelica.university/behavior/equations/first_order/
Thank you
From Calculus, time derivative of x (i.e. dx/dt (t0) ) represents the amount of increase or decrease of a variable as simulation proceeds at time point t0. Remember Taylor series expansion:
x(t0 + dt) = x(t0) + dx/dt(t0) . dt + O(dt^2)
So from this Calculus-based observation it is straightforward to see that:
der(x) > 0, then x will increase as the simulation runs and vise versa.x will increase as time increases but der(x) would decrease as x increases.der(x) approaches 0, then the increase of x will slow down and x tends to 1.x is equal to 2, then der(x) = -1 at the start of the simulation and it approaches 0 as time increases and meanwhile x approaches 1.x = 1, then der(x) = 0 and x would neither increase nor decrease. The value of x = 1 is the steady-state of the given ODE system that makes der(x) = 0