I got access to a rather large number of parameters for which this happens. Most notably, the last parameter scales the noise. This error happens for this parameter is 0.001 (very small). Here the noise is essentially negligible.
using StochasticDiffEq
function sys_f(du,u,p,t)
σ,A = u
S,D,τ,v0,n,η = p
du[1] = v0+(S*σ)^n/((S*σ)^n+(D*A)^n+1) - σ
du[2] = τ*(σ-A)
end
function sys_g(du,u,p,t)
σ,A = u
S,D,τ,v0,n,η = p
du[1,1] = η*sqrt(max(v0+(S*σ)^n/((S*σ)^n+(D*A)^n+1),0.))
du[1,2] = -η*sqrt(max(σ,0.))
du[1,3] = 0
du[1,4] = 0
du[2,1] = 0
du[2,2] = 0
du[2,3] = η*sqrt(max(τ*σ,0.))
du[2,4] = -η*sqrt(max(τ*A,0.))
end
u0 = [0.025, 0.025]
tspan = (0.,200.)
p = [6.7341506577508214, 1.2224984640507832, 0.05, 0.025, 3.0, 0.001]
sde_prob = SDEProblem(sys_f,sys_g,u0,tspan,p,noise_rate_prototype=zeros(2,4));
sol1 = solve(sde_prob,ImplicitEM(),seed=5105556673070507935); sol = sol1;
sol2 = solve(sde_prob,ImplicitEM());
┌ Warning: Interrupted. Larger maxiters is needed.
└ @ DiffEqBase /home/torkelloman/.julia/packages/DiffEqBase/V7P18/src/integrator_interface.jl:329
using Plots
gr(); default(fmt = :png);
p1 = plot(sol1,framestyle=:box,title="Bad stuff",xlimit=(0.,sol1.t[end]))
p2 = plot(sol2,framestyle=:box,title="Everything is fine",xlimit=(0.,sol1.t[end]))
p3 = plot(sol2,framestyle=:box,title="Everything is fine",xlimit=(0.,sol2.t[end]))
plot_trajectories = plot(p1,p2,p3,size=(1200,400),layout=(1,3))
p1 = plot(sol1.t[2:end],diff(sol1.t),framestyle=:box,xlimit=(0.,sol1.t[end]),title="Bad stuff")
p2 = plot(sol2.t[2:end],diff(sol2.t),framestyle=:box,xlimit=(0.,sol1.t[end]),title="Everything is fine")
p3 = plot(sol2.t[2:end],diff(sol2.t),framestyle=:box,xlimit=(0.,sol2.t[end]),title="Everything is fine")
plot_dts = plot(p1,p2,p3,size=(1200,400),layout=(1,3))
Happy to provide any more info!