See a list of demos on

http://ddebiftool.sourceforge.net/demos/index.html

To get started, it is best to run first one of the demos, and then adapt it for the system you want to study.

You will see what kind of continuation you can make, such as steady state continuation, periodic solutions, two-parameter bifurcation continuations, etc.

Delays-there can be several of them-can be used as bifurcation parameters like any other parameters.

Thank you for your suggestion 

I have tried the bifurcation code which you have been suggested but i get the error message 

When I define funcs then if i run to call the value, the error message occurs as

?? Undefined function or variable 'funcs'

But the funcs  file is defined.

Please Help me to rectify this error and to solve further.. 

I just checked the latest version of dde-biftool (v3.1) and all the demos are included in the distribution. Did you try to run for instance the demo in the folder dde_biftool_v3.1/demos/neuron? If you launch the demo with the command rundemo, it works perfectly until I get an error 'struct2array' undefined. I am using matlab 2012. The variable funcs you mention is a struct, I think this should be mostly compatible with matlab 2010, but maybe not. Try to see if you can define funcs as in the demo. 

You can also use XPPAUT to draw bifurcation diagram.

i would recommend Mathematica's built-in solver (no external "tool box" needed). 

https://reference.wolfram.com/language/tutorial/NDSolveDelayDifferentialEquations.html

I am also beginning to use ddebiftool. As pointed above, there are many examples provided with the package. However,  these examples are basically assuming the dynamical nature of the system you have is already pretty much known to you. In other words, the examples assume you know what to look for in the dynamics and they show you how to use the utilities to determine and beautifully display the dynamics. This is all fine. But if you do not know a priori anything about the nature the dynamics in your system, in other words, if your system is not a textbook example, using this set of functions to truly explore is a little hard and definitely slow going. In my case, I got into a tangle of Matlab errors due to vectorization; so rather than fight windmills, for the time being, I turned vectorization off. Then it proceeded slower but much steadier until:

indhopf =

14

indTakens =

Empty matrix: 1-by-0

maximal L1 along branch2: -0.0185043

max error of L1 along branch2: 3.33646e-007

BR_CONTN warning: boundary hit.

Loss of stability at point 1

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =

3.761348e-025.

> In p_correc at 250

In correct_ini at 35

In SetupPOfold at 106

In ds1R_4D_2 at 332

it=1, res=2.95258e-011

...

it=5, res=0.00882611

Warning: Correction failed

> In correct_ini at 39

In SetupPOfold at 106

In ds1R_4D_2 at 332

Error using br_contn (line 38)

BR_CONTN: could not start branch, length=1.

Error in ds1R_4D_2 (line 339)

branch5=br_contn(foldfuncs,branch5,100);

So after finding a Hopf, after following oscillations in two parameters (one of which is a delay), it gave up .   It seemed very exciting for a while, but now I am at loss what to do. Some of the simple example does not seem to apply to my system, so I am not sure this part of the problem is even relevant or not. I know there is a Hopf, I would be happy with a diagram showing how the hopf varies in two parameters (I have that already actually) and how oscillations grow from it (this is where the  problem occurs). Any hints would be very appreciated.

Hi Marc,

Did you manage to follow the Hopf at all? Or did the branch continuation fail immediately? 

You have a warning of badly scaled matrix. This might come from an error in the sys_deri.m file (some derivatives are 0 when they shouldn't). Not all derivative are needed to follow branches so you may be able to do a lot before you run into an error. My experience is that 90% of the errors are from there. 

Hi Sam, 

Okay thank you

I have a question. There are many m.files in dde biftool. How can I run the examples in it. It seems too many files. I am also confused how dde biftool works, and it is very different with matcont for ODE

Dear, Tianyu Cheng

The first 4 file in the Neuron Demo are the main files for Double Hopf Bifurcation of Delay Differential Equations.

Dear, Velmurugan Gandhi

First of all you have to find the equilibrium points of your model on the value given parameters. Then in second file of Neuron demo you have to put the RHS of your model. Specify the position of delays. Then choose two parameters as BIFURCATION parameters. Then in third file you have to put all the value of parameters and equilibrium points. Vary the value of Bifurcation parameters and run.