SDESystem

System Constructors

ModelingToolkit.SDESystemType
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. Must not contain the independent variable.

  • ps

    Parameter variables. Must not contain the independent variable.

  • 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.

  • 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

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])

To convert an ODESystem to an SDESystem directly:

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

Composition and Accessor Functions

  • get_eqs(sys) or equations(sys): The equations that define the SDE.
  • get_states(sys) or states(sys): The set of states in the SDE.
  • get_ps(sys) or parameters(sys): The parameters of the SDE.
  • get_iv(sys): The independent variable of the SDE.

Transformations

Missing docstring.

Missing docstring for structural_simplify. Check Documenter's build log for details.

Missing docstring.

Missing docstring for alias_elimination. Check Documenter's build log for details.

Analyses

Applicable Calculation and Generation Functions

calculate_jacobian
calculate_tgrad
calculate_factorized_W
generate_jacobian
generate_tgrad
generate_factorized_W
jacobian_sparsity

Problem Constructors

Missing docstring.

Missing docstring for SDEFunction. Check Documenter's build log for details.

Missing docstring.

Missing docstring for SDEProblem. Check Documenter's build log for details.