I have the following system of differential equations:
$$ x' = ax- cy + e1 $$
$$y' = by- dx + e2 $$
for variables $x,y$ and parameters $a,b,c,d,e1,e2$.
I'd like to solve this in python, which is easy enough with
def f(y, t, params): weaponsC1, weaponsC2 = y a, b, c, d, e1, e2 = params t_0 = 10 t_1 = 11 derivs = [a*x- c*y + e1, b*y - d*x + e2] return derivs #solve psoln = odeint(f, y0, t, args=(params,), rtol=1e-10)
This returns what you'd expect:
$$a = 1\\ b = 1 \\ c = 2 \\ d = 2 \\ e1 = 5 \\ e2 = 5$$
and initial condition: $(2,2)$, the code above returns:
Now I'd like to add a forcing function $g$ such that I can perturb the ODE by some constant amount at some time. After a bit of a struggle with neater methods, I settled on doing it like this:
def f(y, t, params): weaponsC1, weaponsC2 = y a, b, c, d, e1, e2 = params t_0 = 10 t_1 = 11 derivs = [a*weaponsC1- c*weaponsC2 + e1, + (2*(t > t_0)*(t < t_0+0.5)) + (5*(t > t_1)*(t < t_1+0.5)), b*weaponsC2 - d*weaponsC1 + e2 + (2*(t > t_0)*(t < t_0+0.5))+ (5*(t > t_1)*(t < t_1+0.5))] return derivs
A graph of just the forcing function is shown, thought at different time value:
def g(t_0): return((2*(t > t_0)*(t < t_0+0.5))) plt.plot(t,(g(3) + g(4)))
when I plot the ODE with this forcing function, it works fine for any initial condition which is not the equilibrium:
However, when I set the equilibrium as the starting condition, try as I may, I can never impact the ODE:
this is the same code that made the above working solution; the only change is the starting condition.
I know ODEint assumes the diffeq is differentiable, and mine is not — could this be the cause of the issue? Or is this the result of some property of the ODE?