y_petri

YPetri

YPetri is a domain model and a simulator of dynamical systems. It was inspired by the problems from the field of modelling of biochemical pathways, but on purpose, YPetri is not specific to biochemistry. As a matter of separation of concerns, YPetri caters solely to the two main concerns of modelling, model specification and simulation, excelling in the first one. YPetri implements a novel universal Petri net type, that integrating discrete/continous, deterministic/stochastic, timed/timeless and stoichiometric/nonstoichiometric dichotomies commonly seen in extended Petri nets. YPetri allows specification of any kind of dynamical system whatsoever.

Usage

YPetri provides a domain specific language (DSL) that can be loaded by:

  require 'y_petri'
  include YPetri

(As a matter of terminology, DSLs used in modelling are sometimes termed domain specific modelling languages (DSMLs). This term is popular especially in engineering.) Petri net places can now be created:

  A = Place()
  B = Place()
  places.names # you can shorten this to #pn
  #=> [:A, :B]
  # Setting their marking:
  A.marking = 2
  B.marking = 5

And transitions:

  A2B = Transition stoichiometry: { A: -1, B: 1 }
  #=> #<Transition: A2B (tS) >
  A2B.stoichiometry
  #=> [-1, 1]
  A2B.s
  #=> {:A=>-1, :B=>1}
  A2B.arcs.names
  #=> [:A, :B]
  A2B.timeless?
  #=> true
  A2B.enabled?
  #=> true

Explanation of the keywords: arcs, enabled are standard Petri net terms, stoichiometry means arcs with the amount of tokens to add / take from the connected places when the transition fires, timeless means that firing of the transition is not defined in time.

We can now play the token game:

  places.map &:marking
  #=> [2, 5]
  A2B.fire!
  places.map &:marking
  #=> [1, 6]
  A2B.fire!
  places.map &:marking
  #=> [0, 7]

Advanced usage

A Petri net is mostly used as a wiring diagram of some real-world system. Such Petri net can then be used to generate its simulation -- represented by YPetri::Simulation class. A Petri net consisting of only timed transitions can be used to generate (implicitly or explicitly) a system of ordinary differential equations (ODE). A simulation generated from such Petri net can then be used to solve (eg.) the initial value problem by numeric methods:

  # Start a fresh irb session!
  require 'y_petri'
  include YPetri
  A = Place default_marking: 0.5
  B = Place default_marking: 0.5
  A_pump = Transition s: { A: -1 }, rate: proc { 0.005 }
  B_decay = Transition s: { B: -1 }, rate: 0.05
  net
  #=> #<Net: name: Top, 2pp, 2tt >
  run!

Simulation can now be accessed through simulation DSL method:

  simulation
  #=> #<Simulation: time: 60, pp: 2, tt: 2, oid: -XXXXXXXXX>
  simulation.settings
  #=> {:method=>:pseudo_euler, :guarded=>false, :step=>0.1, :sampling=>5, :time=>0..60}
  print_recording

If you have gnuplot gem installed properly, you can view plots:

  plot_state
  plot_flux

Gillespie method

To try out another simulation method, Gillespie algorithm, open a fresh session and type:

require 'y_petri'
require 'sy'
require 'mathn'
include YPetri

A = Place m!: 10
B = Place m!: 10
AB = Place m!: 0
AB_association = Transition s: { A: -1, B: -1, AB: 1 }, rate: 0.1
AB_dissociation = Transition s: { AB: -1, A: 1, B: 1 }, rate: 0.1
A2B = Transition s: { A: -1, B: 1 }, rate: 0.05
B2A = Transition s: { A: 1, B: -1 }, rate: 0.07

set_step 1
set_target_time 50
set_sampling 1
set_simulation_method :gillespie

run!

print_recording

Again, you can visualize the results using gnuplot gem:

  plot_state

So much for the demo for now! Thanks for trying YPetri!

Contributing

• Fork it
• Create your feature branch (git checkout -b my-new-feature)
• Commit your changes (git commit -am 'Added some feature')
• Push to the branch (git push origin my-new-feature)
• Create new Pull Request core_ext/array/