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JumpSystem

System Constructors

ModelingToolkit.JumpSystem — Type
struct JumpSystem{U<:RecursiveArrayTools.ArrayPartition} <: AbstractTimeDependentSystem

A system of jump processes.

Fields

  • tag: A tag for the system. If two systems have the same tag, then they are structurally identical.
  • eqs: The jumps of the system. Allowable types are ConstantRateJump, VariableRateJump, MassActionJump.

  • iv: The independent variable, usually time.

  • unknowns: The dependent variables, representing the state of the system. Must not contain the independent variable.

  • ps: The parameters of the system. Must not contain the independent variable.

  • var_to_name: Array variables.

  • observed: Observed variables.

  • name: The name of the system.

  • systems: The internal systems. These are required to have unique names.

  • defaults: The default values to use when initial conditions and/or parameters are not supplied in ODEProblem.

  • connector_type: Type of the system.
  • discrete_events: A Vector{SymbolicDiscreteCallback} that models events. Symbolic analog to SciMLBase.DiscreteCallback that executes an affect when a given condition is true at the end of an integration step. Note, one must make sure to call reset_aggregated_jumps!(integrator) if using a custom affect function that changes any unknown value or parameter.
  • parameter_dependencies: A mapping from dependent parameters to expressions describing how they are calculated from other parameters.
  • metadata: Metadata for the system, to be used by downstream packages.
  • gui_metadata: Metadata for MTK GUI.
  • complete: If a model sys is complete, then sys.x no longer performs namespacing.
  • index_cache: Cached data for fast symbolic indexing.

Example

using ModelingToolkit, JumpProcesses

@parameters β γ
@variables t S(t) I(t) R(t)
rate₁   = β*S*I
affect₁ = [S ~ S - 1, I ~ I + 1]
rate₂   = γ*I
affect₂ = [I ~ I - 1, R ~ R + 1]
j₁      = ConstantRateJump(rate₁,affect₁)
j₂      = ConstantRateJump(rate₂,affect₂)
j₃      = MassActionJump(2*β+γ, [R => 1], [S => 1, R => -1])
@named js      = JumpSystem([j₁,j₂,j₃], t, [S,I,R], [β,γ])
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Composition and Accessor Functions

  • get_eqs(sys) or equations(sys): The equations that define the jump system.
  • get_unknowns(sys) or unknowns(sys): The set of unknowns in the jump system.
  • get_ps(sys) or parameters(sys): The parameters of the jump system.
  • get_iv(sys): The independent variable of the jump system.
  • discrete_events(sys): The set of discrete events in the jump system.

Transformations

ModelingToolkit.structural_simplify — Function
structural_simplify(sys; ...)
structural_simplify(sys, io; simplify, split, kwargs...)

Structurally simplify algebraic equations in a system and compute the topological sort of the observed equations. When simplify=true, the simplify function will be applied during the tearing process. It also takes kwargs allow_symbolic=false and allow_parameter=true which limits the coefficient types during tearing.

The optional argument io may take a tuple (inputs, outputs). This will convert all inputs to parameters and allow them to be unconnected, i.e., simplification will allow models where n_unknowns = n_equations - n_inputs.

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Analyses

Problem Constructors

Missing docstring.

Missing docstring for DiscreteProblem(sys::JumpSystem, u0map, tspan). Check Documenter's build log for details.

JumpProcesses.JumpProblem — Method
DiffEqBase.JumpProblem(js::JumpSystem, prob, aggregator; kwargs...)

Generates a JumpProblem from a JumpSystem.

Continuing the example from the DiscreteProblem definition:

jprob = JumpProblem(complete(js), dprob, Direct())
sol = solve(jprob, SSAStepper())
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