Simulating the system

trajectory(ds::DynamicalSystem, T [, u0]; kwargs...) → X, t

Evolve ds for a total time of T and return its trajectory X, sampled at equal time intervals, and corresponding time vector. X is a StateSpaceSet. The returned time vector is t = (t0+Ttr):Δt:(t0+Ttr+T).

Optionally provide a starting state u0 which is current_state(ds) by default.

If time evolution diverged or in general failed before T, the remaining of the trajectory is set to the last valid point.

The dimensions of X are automatically named if ds referrences an MTK model and if save_idxs remains at its default value.

Keyword arguments

• Δt: Time step of value output. For discrete time systems it must be an integer. Defaults to 0.1 for continuous and 1 for discrete time systems. If you don't have access to unicode, the keyword Dt can be used instead.
• Ttr = 0: Transient time to evolve the initial state before starting saving states.
• t0 = initial_time(ds): Starting time.
• container = SVector: Type of vector that will represent the state space points that will be included in the StateSpaceSet output. See StateSpaceSet for valid options.
• save_idxs: Which variables to output in X. By default it is nothing (all variables). It can be a vector of any type of index that can be given to observe_state. Note: if you mix integer and symbolic indexing be sure to initialize the array as Any so that integers 1, 2, ... are not converted to symbolic expressions.

Description

trajectory is a very simple function provided for convenience. For continuous time systems, it doesn't play well with callbacks, use DifferentialEquations.solve if you want a trajectory that works with callbacks, or in general you want more flexibility in the generated trajectory (but remember to convert the output of solve to a StateSpaceSet).

deterministic_orbit(
    sys::CoupledSDEs,
    T;
    ...
) -> Tuple{Any, Any}
deterministic_orbit(
    sys::CoupledSDEs,
    T,
    init;
    diffeq,
    kwargs...
) -> Tuple{Any, Any}

Simulates the deterministic (noise-free) dynamics of CoupledSDEs sys in time for a duration T, starting at initial condition init.

This function is equivalent to calling trajectory on the deterministic part of the CoupledSDEs (with noise_strength=0). It works with the ODE solvers used for CoupledODEs.

Keyword arguments

• diffeq=(alg=Tsit5(), abstol = 1e-6, reltol = 1e-6): ODE solver settings (see CoupledODEs)
• kwargs...: keyword arguments passed to trajectory

For more info, see ODEProblem. For stochastic integration, see trajectory.