using Catlab, Catlab.Graphics
using AlgebraicPetri
using OrdinaryDiffEq, Plots
using LabelledArrays

The Brusselator

This notebook creates a Petri net for a Brusselator reaction network:

$$ A \rightarrow X$$$$ 2X + Y \rightarrow 3X$$$$ B + X \rightarrow Y + D$$$$ X \rightarrow E$$

In comparison to the reaction net above, our Petri net adds in an output arc from the t1 transition to the A species and from the t3 transition to the B in order to keep the concentrations of A and B constant. This is a common property in simulations

Brusselator= LabelledPetriNet([:A, :B, :D, :E, :X, :Y], 
    :t1 => (:A => (:X, :A)),
    :t2 => ((:X, :X, :Y) => (:X, :X, :X)),
    :t3 => ((:B, :X) => (:Y, :D, :B)),
    :t4 => (:X => :E)
)

Graph(Brusselator)

u0 = LVector(A = 1., B = 3., D = 0., E = 0., X = 1., Y = 1.)
p = LVector(t1 = 1., t2 = 1., t3 = 1., t4 = 1.)
tspan = (0.0, 40.0)

Brusselator_vf = vectorfield(Brusselator)
prob = ODEProblem(Brusselator_vf, u0, tspan, p)
sol = solve(prob, Tsit5())

plot(sol, vars = [5,6], lw = 2)