Bifurcation Diagram Files

Using the commandParseDiagramFile command (Section 4.14.18 in the reference) the user can parse and read into memory an AUTO bifurcation diagram file. For example, the command commandParseDiagramFile('ab') would parse the file b.ab (if you are using the standard filename translations from Table 4.3) and return an object which encapsulates the bifurcation diagram in an easy to use form.

The object returned by the commandParseDiagramFile is a list of all of the solutions in the appropriate bifurcation diagram file, and each solution is a Python dictionary with entries for each piece of data for the solution. For example, the sequence of commands in Figure 4.14, prints out the label of the first solution in a bifurcation diagram. The queriable parts of the object are listed in Table 4.4.

The individual elements of the array may be accessed in two ways, either by index of the solution using the [] syntax or by label number using the () syntax. For example, assume that the parsed object is contained in a variable data. The first solution may be accessed using the command data[0], while the solution with label 57 may be accessed using the command data(57).

Table 4.4: This table shows the strings that can be used to query a bifurcation diagram object and their meanings.

Query string	Meaning
TY name	The short name for the solution type (see Table 4.5).
TY number	The number of the solution type (see Table 4.5).
BR	The branch number.
PT	The point number.
LAB	The solution label, if any.
section	A unique identifier for each branch in a file with multiple branches.
data	An array which contains the AUTO output.

Table 4.5: This table shows the the various types of points that can be in solution and bifurcation diagram files, with their short names and numbers.

Type	Short Name	Number
No Label	No Label
Branch point (algebraic problem)	BP	1
Fold (algebraic problem)	LP	2
Hopf bifurcation (algebraic problem)	HB	3
Regular point (every NPR steps)	RG	4
User requested point	UZ	-4
Fold (ODE)	LP	5
Bifurcation point (ODE)	BP	6
Period doubling bifurcation (ODE)	PD	7
Bifurcation to invarient torus (ODE)	TR	8
Normal begin or end	EP	9
Abnormal termination	MX	-9