### Legend ###
KGTI - Kerr Gires-Tournois interferomter
APE - Alternating profile equation
SW - Square wave


### main ###
Contains demo files that can be executed with matlab
	
	S1: How to get an APE branch from a KGTI branch
		A point is selected from a KGTI SW branch. 
		To get an extended solution point for the APE, the profile needs to be shifted by half the period.
		The extended solution now consists of the original and the shifted profile together.
		The period rho for the APE point can be calculated from difference of the original period T and twice the delay tau as rho=0.5*(T-tau).
		Now, as the delay is supposed to be a new variable, we need to fix the period.
		Finally, however, the APE system can be treated as any other system that is implemented in ddebiftool.

	S2: How to get a branch of relative homoclinics from an APE branch
		To get a profile for a relative homoclinic, one starts from a SW solution of an APE branch.
		First, the equilibria have to be selected. Here, this has been done visually. 
		As the mesh goes from 0 to 1 we can plot the profile and look, where the plateaus are setteled.
		In this example, these values are, e.g., 0.25 and 0.7 of the mesh. 
		Now the profile has to be selected. The profile has to contain the transition between the chosen equilibria.
		This is our initial guess which is converted to a connecting orbit with complex eigenpairs.
		Finally, we create a branch with data type 'comp_hcli' and continuate it using ddebiftool functions.
	
	S3: How to continuate a Bykov-T point that occurs along the APE branch from a point in its surrounding
		The initial guess for a Bykov-T point is created similar to the one of a relative homoclinic.
		Instead of two, three equilibria P1, P2 and P3 are selected.
		Additionally, two transitions P1-P2 and P2-P3 are taken as profiles.
		Both are corrected as simple heteroclinic orbits.
		The initial guess 'bykov_init' combines both heteroclinic orbits.
		Finally, a branch with data type 'bykov' is created.
		It tracks the codimension two bifurcation point where both heteroclinics coexist.		
		

### code ###
Contains dependencies
	KGTI_funcs: System information about the KGTI
	APE_funcs: System information about the APE system
	dde_biftool: Contains the folders of dde_biftool with the delay algebraic equation extension 	that are needed for this study
	Bykov_funcs: Containing additional and modified functions for the continuation of relative homoclinics and Bykov-T points that are a result of our work
	Additional functions: plot_indices.m helps to select points from a branch, integrate_profile.m is the measure used for the KGTI solutions


### Note ###
The code examples are written in a way that they should work as long as the
relative paths remain unchanged.

