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'''
	BifTools v1.1.1
'''

Date: 11.12.2011
Autors: Milen Borisov, Neli Dimitrova
Contacts: milen_kb@abv.bg, nelid@bio.bas.bg
Copyright: (2009-2011) Milen Borisov, Neli Dimitrova.

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Package Description.
BifTools is a package for symbolic and numeric bifurcation analysis of equilibrium 
points in dynamical systems. The package consists of five main procedures: 
 * BifTools[calcOneZeroEigenvalueBifPoints] calculates the bifurcation points 
   of an ODE system with a single zero eigenvalue of the Jacobian;
 * BifTools [calcOneZeroEigenvalueBif] calculates the normal form of the steady 
   states bifurcations with a single zero eigenvalue of the Jacobian;
 * BifTools [calcHopfBifPoints] calculates the Andronov-Hopf bifurcation points 
   of an ODE system, using the method of resultants;
 * BifTools [calcHopfBif] calculates the normal form of the Andronov-Hopf 
   bifurcation of the equilibrium points;
 * BifTools [calcBTBif] calculates the normal form of the Bogdanov-Takens 
   (double zero) bifurcation, using the projection or the direct method for 
   center manifold reduction;

Software Requirements.
Maple 13 or higher versions (http://www.maplesoft.com/products/Maple/index.aspx)

Legal Notice.
The copyright for this application is owned by the authors. Neither Maplesoft 
nor the authors are responsible for any errors contained within and are not 
liable for any damages resulting from the use of this material. This application 
is intended for non-commercial, non-profit use only. Contact the authors for 
permission if you wish to use this application in for-profit activities.

Files included.
Readme.txt - this file.
BifTools.mw - a worksheet with complete code of the BifTools library.
BifTools.mla - a package version of the BifTools library.
BifToolsDoc.mla - a maple document file of the BifTools library.
Examples (folder) - a folder with examples.
html (folder) - a maple document of the BifTools library (html version).



---------------------------------------------------------------------------
			BifTools v1.1.1
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<> Fixed bugs:

* Fixed a bug in the BifExt[getNormEigenVectors] procedure.
Simplified some values before checking them, e.g.
  if (simplify(evals[1]) = simplify(-I*omega) then
  ...
instead of 
  if evals[1] = -I*omega then
  ...

<> New features:

* BifTools[calcOneZeroEigenvalueBif] - a procedure for calculating the steady
 state bifurcation points of an ODEs system.



---------------------------------------------------------------------------
			BifTools v1.1.0
---------------------------------------------------------------------------

<> New features:

* BTBifExt - a package, which contains helful procedures for calculating Bogdanov-
Takens (double zero) bifurcation nomral form.

* BifTools[calcBTBif] - a procedure for calculating Bogdanov-Takens (double zero) 
bifurcation nomral form.



---------------------------------------------------------------------------
			BifTools v1.0.3
---------------------------------------------------------------------------

<> New features:

* HopfBifExt[testGetEigenvaluesOfJacobian] - a procedure, which
returns the eigenvalues of the Jacobian on a ODEs system 
in a Hopf bifurcation point.

* HopfBifResultantExt - a package, which contains helpful procedures for 
calculating Hopf bifurcation points on an ODEs system, using the resultant 
method.

* BifTools[calcHopfBifPoints] - a procedure for calculating Hopf 
bifurcation points on an ODEs system, using the resultant method.

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'''
	Installing BifTools
'''

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If you received BifTools as library file (*.mla), save it in a 
directory of your choice and proceed with "How to load BifTools once the 
library has been created." (see below).

If you received BifTools as a worksheet and did not yet create the 
package library, proceed with "How to create the package BifTools library" 
(see below).



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'''
	How to create the package BifTools library
'''
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Before you start using BifTools the first time, you must create the 
BifTools package library in a file of your choice. 
The following steps have to be done to create the package library:

i) Load the worksheet containing the package (BifTools.mw) into a 
graphical Maple version.

ii) Go to the very end of that worksheet and follow the instructions in 
the section "How to create the BifTools library from this worksheet".



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'''
	How to load BifTools once the library has been created
'''
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Open a new empty worksheet and load the library as follows, replacing 
"<new-library-file>" by the file path you chose to save the library in 
(e.g., Linux: "/usr/maple/mylib/BifTools.mla" or 
Windows: "C:\\Maple\\MyLib\\BifTools.mla").

> restart;
> libname:="<new-library-file>", libname;
> with(BifTools);


!!! ATTENTION:
If you want to configurate the output settings, you can use some of the 
following lines:

>TraceExt:-enable();
>PrintExt:-setVar1SymbolHopfBif('_X'):
>PrintExt:-setVar2SymbolHopfBif('_Y'):
>PrintExt:-setParamSymbolHopfBif('alpha'):
>PrintExt:-setSigma0SymbolHopfBif('sigma[0]');
>PrintExt:-setSigma1SymbolHopfBif('sigma[1]');

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'''
   	Examples
'''

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See: 
Examples_SteadyStateBif.mw
Examples_HophBif.mw
Examples_HopfBif_DEplot.mw
Examples_HopfBif_FindBifurcationPoints.mw
Examples_BTBif.mw

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