EquationTrekker`
EquationTrekker`

PoincareSection

PoincareSection

is a setting for the option TrekGenerator that specifies that the Poincaré section for differential equations is used to generate treks.

Details and Options

  • To use PoincareSection, you first need to load the Equation Trekker Package using Needs["EquationTrekker`"].
  • With TrekGenerator->{PoincareSection,method->value,…} possible method options are:
  • "SectionCondition"Nonewhen section variables will be shown
    "SectionVariables"Nonevariables to be plotted
    "FilterFunction"Nonefunction applied to variables before plotting
  • Options specific to NDSolve may also be included as method options.
  • The method options "SectionCondition" and "SectionVariables" are required to have a value other than None.
  • The method option "SectionCondition"->cond plots section variables whenever cond==0.
  • The setting for the method option "SectionVariables" should be a list of two of the dependent variables. If the differential equations are second order or higher, then derivatives of the dependent variables may also be chosen.
  • With "FilterFunction"->f, the argument supplied to f is a list of the coordinates to be plotted.

Examples

Basic Examples  (1)

This shows an example of treks generated by Duffing's equation:

Generating a Poincaré section for the same equation: