JumpSystem

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 equations.

• name: The name of the system.

• description: A description 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.

• guesses: The guesses to use as the initial conditions for the initialization system.

• initializesystem: The system for performing the initialization.

• initialization_eqs: Extra equations to be enforced during the initialization sequence.

• connector_type: Type of the system.

• continuous_events: A Vector{SymbolicContinuousCallback} that model events. The integrator will use root finding to guarantee that it steps at each zero crossing.

• 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: Topologically sorted parameter dependency equations, where all symbols are parameters and the LHS is a single parameter.

• metadata: Metadata for the system, to be used by downstream packages.

• gui_metadata: Metadata for MTK GUI.

• namespacing: If false, then sys.x no longer performs namespacing.

• complete: If true, denotes the model will not be modified any further.

• index_cache: Cached data for fast symbolic indexing.

• isscheduled

Example

using ModelingToolkit, JumpProcesses
using ModelingToolkit: t_nounits as t

@parameters β γ
@variables 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])

structural_simplify(sys; ...)
structural_simplify(
    sys,
    io;
    additional_passes,
    simplify,
    split,
    allow_symbolic,
    allow_parameter,
    conservative,
    fully_determined,
    kwargs...
)

Structurally simplify algebraic equations in a system and compute the topological sort of the observed equations in sys.

Optional Arguments:

• 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.

Optional Keyword Arguments:

• When simplify=true, the simplify function will be applied during the tearing process.
• allow_symbolic=false, allow_parameter=true, and conservative=false limit the coefficient types during tearing. In particular, conservative=true limits tearing to only solve for trivial linear systems where the coefficient has the absolute value of $1$.
• fully_determined=true controls whether or not an error will be thrown if the number of equations don't match the number of inputs, outputs, and equations.
• sort_eqs=true controls whether equations are sorted lexicographically before simplification or not.

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())