SDESystem

struct SDESystem <: ModelingToolkit.AbstractODESystem

A system of stochastic differential equations.

Fields

• tag

: tag: a tag for the system. If two system have the same tag, then they are structurally identical.

• eqs

: The expressions defining the drift term.

• noiseeqs

: The expressions defining the diffusion term.

• iv

: Independent variable.

• states

: Dependent (state) variables. Must not contain the independent variable.

• ps

: Parameter variables. Must not contain the independent variable.

• tspan

: Time span.

• var_to_name

: Array variables.

• ctrls

: Control parameters (some subset of ps).

• observed

: Observed states.

• tgrad

: Time-derivative matrix. Note: this field will not be defined until calculate_tgrad is called on the system.

• jac

: Jacobian matrix. Note: this field will not be defined until calculate_jacobian is called on the system.

• ctrl_jac

: Control Jacobian matrix. Note: this field will not be defined until calculate_control_jacobian is called on the system.

• Wfact

: Wfact matrix. Note: this field will not be defined until generate_factorized_W is called on the system.

• Wfact_t

: Wfact_t matrix. Note: this field will not be defined until generate_factorized_W is called on the system.

• name

: Name: the name of the system

• systems

: Systems: the internal systems. These are required to have unique names.

• defaults

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

• connector_type

: type: type of the system

• continuous_events

: 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

: discrete_events: A Vector{SymbolicDiscreteCallback} that models events. Symbolic analog to SciMLBase.DiscreteCallback that exectues an affect when a given condition is true at the end of an integration step.

• metadata

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

• complete

: complete: if a model sys is complete, then sys.x no longer performs namespacing.

Example

using ModelingToolkit

@parameters σ ρ β
@variables t x(t) y(t) z(t)
D = Differential(t)

eqs = [D(x) ~ σ*(y-x),
       D(y) ~ x*(ρ-z)-y,
       D(z) ~ x*y - β*z]

noiseeqs = [0.1*x,
            0.1*y,
            0.1*z]

@named de = SDESystem(eqs,noiseeqs,t,[x,y,z],[σ,ρ,β]; tspan = (0, 1000.0))

function DiffEqBase.SDEFunction{iip}(sys::SDESystem, dvs = sys.states, ps = sys.ps;
                                     version = nothing, tgrad=false, sparse = false,
                                     jac = false, Wfact = false, kwargs...) where {iip}

Create an SDEFunction from the SDESystem. The arguments dvs and ps are used to set the order of the dependent variable and parameter vectors, respectively.

function DiffEqBase.SDEProblem{iip}(sys::SDESystem,u0map,tspan,p=parammap;
                                    version = nothing, tgrad=false,
                                    jac = false, Wfact = false,
                                    checkbounds = false, sparse = false,
                                    sparsenoise = sparse,
                                    skipzeros = true, fillzeros = true,
                                    linenumbers = true, parallel=SerialForm(),
                                    kwargs...)

Generates an SDEProblem from an SDESystem and allows for automatically symbolically calculating numerical enhancements.

function DiffEqBase.SDEFunctionExpr{iip}(sys::AbstractODESystem, dvs = states(sys),
                                     ps = parameters(sys);
                                     version = nothing, tgrad=false,
                                     jac = false, Wfact = false,
                                     skipzeros = true, fillzeros = true,
                                     sparse = false,
                                     kwargs...) where {iip}

Create a Julia expression for an SDEFunction from the SDESystem. The arguments dvs and ps are used to set the order of the dependent variable and parameter vectors, respectively.

function DiffEqBase.SDEProblemExpr{iip}(sys::AbstractODESystem,u0map,tspan,
                                    parammap=DiffEqBase.NullParameters();
                                    version = nothing, tgrad=false,
                                    jac = false, Wfact = false,
                                    checkbounds = false, sparse = false,
                                    linenumbers = true, parallel=SerialForm(),
                                    kwargs...) where iip

Generates a Julia expression for constructing an ODEProblem from an ODESystem and allows for automatically symbolically calculating numerical enhancements.