All models with
ODESystem are deterministic.
SDESystem adds another element to the model: randomness. This is a stochastic differential equation which has a deterministic (drift) component and a stochastic (diffusion) component. Let's take the Lorenz equation from the first tutorial and extend it to have multiplicative noise.
using ModelingToolkit, StochasticDiffEq # Define some variables @parameters t σ ρ β @variables x(t) y(t) z(t) D = Differential(t) eqs = [D(x) ~ σ*(y-x), D(y) ~ x*(ρ-z)-y, D(z) ~ x*y - β*z] noiseeqs = [0.1*x, 0.1*y, 0.1*z] de = SDESystem(eqs,noiseeqs,t,[x,y,z],[σ,ρ,β]) u0map = [ x => 1.0, y => 0.0, z => 0.0 ] parammap = [ σ => 10.0, β => 26.0, ρ => 2.33 ] prob = SDEProblem(de,u0map,(0.0,100.0),parammap) sol = solve(prob,SOSRI())