I hope that this question belongs here, since my problem is mostly about the DifferentialEquations package.

I have the following dynamical system:

using DifferentialEquations
function some_dynamics(u,p,t)
du = zeros(length(u))
for i in 1:length(u)
for j in 1:length(u)
du[i] += p[i,j]*u[j]*u[i]
end
end
return du
end

prob = ODEProblem(some_dynamics,u0,tspan,p)
sol = solve(prob)

Is it possible to change the parameter p at some point before tspan[end]?
In pseudo code, I would like to be able to plug in something like if t == 0.5 -> p = ones(4,4)

You may want to try the new PresetTimeCallback, now added by popular request! Just add the time that you want the callback to deploy at and then the affect! on the integrator goes as expected. Use a vector of times if you want multiple call times.

using OrdinaryDiffEq, DiffEqCallbacks, Test
function some_dynamics(u,p,t)
du = zeros(length(u))
for i in 1:length(u)
for j in 1:length(u)
du[i] += p[i,j]*u[j]*u[i]
end
end
return du
end
p = rand(4,4)
startp = copy(p)
u0 = zeros(length(p[1,:])) .+ 0.1
tspan = (0.,1.)
prob = ODEProblem(some_dynamics,u0,tspan,p)
cb = PresetTimeCallback(0.5,integrator -> integrator.p .= rand(4,4))
sol = solve(prob,Tsit5(),callback = cb)
prob = ODEProblem(some_dynamics,u0,tspan,p)
cb = PresetTimeCallback([0.3,0.6],integrator -> integrator.p .= rand(4,4))
sol = solve(prob,Tsit5(),callback = cb)