opens a graphical interface for specifying initial conditions and plotting the resulting numerical solution to the first- or second-order ordinary differential equation eqn for the function x with the independent variable t in the range tmin to tmax.


opens a graphical interface for specifying initial conditions and plotting the resulting numerical solution to the system of two first-order ordinary differential equations eqns for the functions x and y.


reopens a graphical interface with the treks saved in the EquationTrekkerState object state.

Details and Options

  • To use EquationTrekker, you first need to load the Equation Trekker Package using Needs["EquationTrekker`"].
  • If eqn is a single first-order ODE, plots of x[t] versus t are displayed. If eqn is a single second-order ODE, plots of x'[t] versus x[t] are displayed. If eqns consist of a system of two first-order ODEs, plots of y[t] versus x[t] are displayed.
  • Treks are invoked by right-clicking a coordinate, which generates a trek that starts at the point specified by the mouse cursor.
  • The initial position of a trek is highlighted in yellow, and by default corresponds to an initial condition specified at t=0. However, only the section of the trek from tmin to tmax is displayed, with the coordinate associated with tmin displayed as a point and the coordinate associated with tmax displayed as an arrowhead.
  • Changing defaults for newly created treks may be accomplished by typing a value in the text field and clicking the _(GraphicsData[CompressedBitmap, eJx1k81rE1EUxU8+Rl10Kbjtxv/CtYrQpeA2FGmL37W7UleCgi4EUXBXLIIo]
                               xC8wePil) button.
  • EquationTrekker generates a modal dialog, and the kernel is controlled by the graphical interface until the window is closed.
  • When the window is closed, a list containing an EquationTrekkerState object and a graphic is returned. The EquationTrekkerState object contains all of the information necessary to reopen the window with the treks that were displayed when the window was closed.
  • The following options can be given:
  • ImageSize{400,400}absolute size of EquationTrekker window
    PlotRange{Automatic,{-1,1}}range of values to include
    TrekParameters {}list of parameters and parameter ranges
    TrekGeneratorDifferentialEquationTrekmethod used to generate treks
  • A valid setting for TrekParameters is a list of rules of the form param->range, where range consists of a starting value and a range, {v,{vmin,vmax}}. The range specification may also consist of a single value v, which is equivalent to {v,{0,2v}}.
  • Valid settings for TrekGenerator are DifferentialEquationTrek and PoincareSection.
  • The default setting TrekGenerator->DifferentialEquationTrek creates treks by following the path of the dependent variables generated using NDSolve.
  • The setting TrekGenerator->PoincareSection creates treks by sampling the phase space. The sampling interval is typically periodic.
  • The setting TrekGenerator->{method,subopts} may be used to include the suboptions subopts for the TrekGenerator method method.


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Basic Examples  (1)

This is a simple example demonstrating how EquationTrekker operates:

A window similar to the one below will appear (but with an empty canvas). Click the canvas to add treks:

Options  (1)

TrekParameters  (1)

This shows a nonlinear perturbation of the simple harmonic oscillator with sliders for α and ω: