SDESystem

System Constructors

ModelingToolkit.SDESystem — Type

struct SDESystem <: ModelingToolkit.AbstractODESystem

A system of stochastic differential equations.

Fields

eqs
The expressions defining the drift term.
noiseeqs
The expressions defining the diffusion term.
iv
Independent variable.
states
Dependent (state) variables.
ps
Parameter variables.
pins
observed
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.

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

Example

using ModelingToolkit

@parameters t σ ρ β
@variables x(t) y(t) z(t)
@derivatives D'~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]

de = SDESystem(eqs,noiseeqs,t,[x,y,z],[σ,ρ,β])

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Composition and Accessor Functions

sys.eqs or equations(sys): The equations that define the SDE.
sys.states or states(sys): The set of states in the SDE.
sys.parameters or parameters(sys): The parameters of the SDE.
sys.iv or independent_variable(sys): The independent variable of the SDE.

Transformations

Applicable Calculation and Generation Functions

calculate_jacobian
calculate_tgrad
calculate_factorized_W
generate_jacobian
generate_tgrad
generate_factorized_W
jacobian_sparsity

Problem Constructors

DiffEqBase.SDEFunction — Type

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.

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DiffEqBase.SDEProblem — Type

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.

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