SDESystem

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.

• 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

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])