@Axel Vogt Thank you for your reply.

I do the same as you said. But I am not get the root of ' w '.

I want to find the value of w.

@Axel Vogt  Thank you for your reply. Now I am change our derivation part and run the code by the above said procedure. but it does not give result. Please help me.... to rectify the error. Thank you. The code is given bellow:

bif.mw

@Axel Vogt Thanks for your kind reply. But I need only the root of the equation not a graph. In the above coding, we assign value for ' sqrt(V) '. Without the 'sqrt(V)' the program gives the root value of ' w '. So, the calculation of sqrt(V) is not correctly given please do the need ful. Thank you.  

@Carl Love Thank you.

Our system is dynamical system with time delay. Also continuous system not discrete.

Thus, the system changes with respect to time t.

@Carl Love 

Please see the following link:

http://www.uow.edu.au/~mnelson/teaching.dir/math111.dir/code.dir/bifurcation-ricker.html

In this similar as my delay differential equation. 

@Carl Love Thanks for your answer.

Please see the following link:

http://www.mapleprimes.com/questions/200459-Bifurcation-Diagram

I think, the posted answer  by you.

In this link show a bifurcation diagram for the parameter ' r ' Vs  ' x '.

The similar, we need the bifurcation diagram for our system between the parameter ' tau ' Vs 'x'.

That's it.

Thanks in Advace. If any query please message me.

@Carl Love Thanks for your answer. The initial conditions are given below

x(0)=2.6; y(0)=1.7; z(0)=0.8; 

How to code for bifurcation by varying parameter tau Versus x(t).