Package PyDSTool :: Package PyCont :: Module Continuation :: Class HopfCurveTwo
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Class HopfCurveTwo

source code

  object --+    
           |    
Continuation --+
               |
              HopfCurveTwo

Child of Continuation class that represents curves of Hopf points.

Augmented system h(x,a): Uses double bordering on the matrix A given by

        A = f_{x}^{2}(x,a) + _k*I_{n}

    (see class PyCont.TestFunc.BorderMethod)
    (see class PyCont.TestFunc.Hopf_Double_Bor_Two)

    The continuation variables are (x,a,_k) with

        x = State variables
        a = Free parameters
        _k = w^2 = Square of pure imaginary eigenvalue associated with Hopf point
            (auxiliary parameter)

    and the continuation curve is defined by

                    { f(x,a) = 0
        h(x,a,_k) = { G_{1,1}(x,a,_k) = 0
                    { G_{2,2}(x,a,_k) = 0

Detection of points: BT, ZH, GH

Instance Methods [hide private]
 
__init__(self, model, gen, automod, plot, args=None)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature
source code
 
update(self, args)
Update parameters for HopfCurveTwo.
source code
 
_createTestFuncs(self)
Creates processors and test functions for HopfCurveTwo class.
source code

Inherited from Continuation: __copy__, __deepcopy__, __repr__, __str__, backward, cleanLabels, computeEigen, display, exportGeomview, forward, getSpecialPoint, info, reset, testdomain, testdomaingrid, testdomaintangrid

Inherited from object: __delattr__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __setattr__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, model, gen, automod, plot, args=None)
(Constructor)

source code 

x.__init__(...) initializes x; see x.__class__.__doc__ for signature

Overrides: object.__init__
(inherited documentation)

update(self, args)

source code 

Update parameters for HopfCurveTwo.

Overrides: Continuation.update

_createTestFuncs(self)

source code 

Creates processors and test functions for HopfCurveTwo class.

Note: In the following list, processors are in PyCont.Bifpoint and test functions are in PyCont.TestFunc.

Point type (Processor): Test function(s) ----------------------------------------------

BT (BTPoint): BT_Hopf ZH (ZHPoint): Fold_Det (or Fold_Bor) GH (GHPoint): GH_Hopf

Overrides: Continuation._createTestFuncs