# Ensure solution stays at zero

**URL:** <https://discourse.julialang.org/t/ensure-solution-stays-at-zero/77482>\
**Category:** General Usage\
**Tags:** diffeq, ode, diffeqcallbacks\
**Created:** [March 6, 2022, 9:57pm UTC](https://discourse.julialang.org/t/ensure-solution-stays-at-zero/77482 "2022-03-06T21:57:50Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![colebrookson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/colebrookson/32/19567_2.png) [@colebrookson](https://discourse.julialang.org/u/colebrookson)\
**Post date:** [March 6, 2022, 9:57pm UTC](https://discourse.julialang.org/t/ensure-solution-stays-at-zero/77482/1 "2022-03-06T21:57:50Z")

</div>

I’m using a `VectorContinuousCallback` to perform an “extinction event”, where for my large 50-equation system, if the values of one species (i’m modeling a bunch of interacting species) goes below 10e-30 then the value of that species goes to zero.

Here’s a mini example of sort of how I’m doing this with a higher threshold:

```julia
function dynamics!(du,u,p,t)
  α, β, γ, δ = p
  du[1] = (α - β * u[2]) * u[1]
  du[2] = (-γ + δ * u[1]) * u[2]
end

function condition(out, u , t, integrator)
  out[1] = 20-u[1]
  out[2] = 20-u[2]
end

function affect!(integrator, idx)
  for i in 1:2
    if idx == i
      integrator.u[i] = 0
    end 
  end 
end

cb = VectorContinuousCallback(condition,affect!,2)

u0 = [100, 100]
p = [0.55, 0.028, 0.84, 0.026]
tspan = (0.0,20.0)
prob = ODEProblem{true}(dynamics!,u0,tspan,p)
sol = solve(prob,Tsit5(), callback = cb)
plot(sol)

```

Which gives me this:  
 ![Screenshot from 2022-03-06 16-51-07](https://global.discourse-cdn.com/julialang/original/3X/d/4/d4fcd163e32ea7d6ca62fa279723aa9a7212a41f.png)  
which is what I want.

However, in a few of my simulations in my larger system (with 50 species and where the extinction threshold is 10e–30, I’ve noticed that values that were taken to zero would sometimes pop back up (i.e. to something small like 2.5e-29 or something), but this is messing with my counting of how many extant species I have in the system.

**My question is: How do I keep a value at zero once it’s been taken there by a callback?** I first thought that I might want to resize the system with `deleteat!` but that causes problems since all the equations are linked.

For now, within my `dynamics!` function I put a condition, so it is like this:

```julia
function dynamics!(du,u,p,t)
    for i in 1:2
       if u[i] < 10e-30
          du[i] = 0.0
          u[i] = 0.0
       else
         *populate du*
    end 
end

```

and I think that worked, but there must be a more elegant way to do this in the solver options?

To be clear, 99% of the time, the value stays at zero, but I need to make sure it does so 100% of the time over millions of sims.

Any thoughts/help much appreciated!!!

Cheers