feat: implement and test SII interface for non-markovian systems

Author: AayushSabharwal

src/systems/abstractsystem.jl

@@ -840,6 +840,8 @@ end
 SymbolicIndexingInterface.is_time_dependent(::AbstractTimeDependentSystem) = true
 SymbolicIndexingInterface.is_time_dependent(::AbstractTimeIndependentSystem) = false
 
+SymbolicIndexingInterface.is_markovian(sys::AbstractSystem) = !is_dde(sys)
+
 SymbolicIndexingInterface.constant_structure(::AbstractSystem) = true
 
 function SymbolicIndexingInterface.all_variable_symbols(sys::AbstractSystem)

test/dde.jl

@@ -39,6 +39,7 @@ eqs = [D(x₀) ~ (v0 / (1 + beta0 * (x₂(t - tau)^2))) * (p0 - q0) * x₀ - d0
        D(x₂(t)) ~ (v1 / (1 + beta1 * (x₂(t - tau)^2))) * (1 - p1 + q1) * x₁ - d2 * x₂(t)]
 @mtkbuild sys = System(eqs, t)
 @test ModelingToolkit.is_dde(sys)
+@test !is_markovian(sys)
 prob = DDEProblem(sys,
     [x₀ => 1.0, x₁ => 1.0, x₂(t) => 1.0],
     tspan,
@@ -81,6 +82,7 @@ sol = solve(prob, RKMil())
 eqs = [D(x(t)) ~ a * x(t) + b * x(t - τ) + c + (α * x(t) + γ) * η]
 @mtkbuild sys = System(eqs, t)
 @test ModelingToolkit.is_dde(sys)
+@test !is_markovian(sys)
 @test equations(sys) == [D(x(t)) ~ a * x(t) + b * x(t - τ) + c]
 @test isequal(ModelingToolkit.get_noiseeqs(sys), [α * x(t) + γ])
 prob_mtk = SDDEProblem(sys, [x(t) => 1.0 + t], tspan; constant_lags = (τ,));
@@ -106,8 +108,10 @@ eqs = [osc1.jcn ~ osc2.delx,
 @named coupledOsc = System(eqs, t)
 @named coupledOsc = compose(coupledOsc, systems)
 @test ModelingToolkit.is_dde(coupledOsc)
+@test !is_markovian(coupledOsc)
 @named coupledOsc2 = System(eqs, t; systems)
 @test ModelingToolkit.is_dde(coupledOsc2)
+@test !is_markovian(coupledOsc2)
 for coupledOsc in [coupledOsc, coupledOsc2]
     local sys = structural_simplify(coupledOsc)
     @test length(equations(sys)) == 4

test/odesystem.jl

@@ -1399,6 +1399,8 @@ end
     @variables x(t)
     @named sys = ODESystem(D(x) ~ x, t)
     @test !ModelingToolkit.is_dde(sys)
+    @test is_markovian(sys)
     @named sys2 = ODESystem(Equation[], t; systems = [sys])
     @test !ModelingToolkit.is_dde(sys)
+    @test is_markovian(sys)
 end