A Mathematical analysis of "My" friendship dynamics :-

With motivations from an earlier post,
http://karthik-4dmspace.blogspot.com/2014/09/memy-social-awkwardness-and-my-only.html
the fictional characters Charlie Eppes,Sheldon Cooper and not to forget the most terrifying device for me in the electronics lab ''THE ZENER DIODE" ,Finally I thought of doing an analysis of "My" Friendship dynamics.

The reverse approach :  This refers to new people who talk to me and how my friendship progresses with them .

Given  the condition that people keep having a conversation with me whenever possible my friendship progresses with them identical to how a zener diode works in its reverse biased condition   till an voltage called  breakdown voltage is given, it doesn't conduct. Similarly until a time (tB)  my friendship doesn't progress with them  ,after (tB) it increases and reaches an extremum and then it becomes constant.

The forward approach : This refers to how I talk with new people ( This according to me is the one and only one problem I cannot solve myself ,in spite of me being a budding mathematician )  and how my friendship progresses with them .

Given  the condition I talk to people,
,the friendship progresses identical to how a zener diode works in its forward biased condition (i.e similar to an ideal diode,it starts conducting.) until, it reaches an extremum and then it becomes constant.

Further with motivation from Shockley Equation for diode : Friendship as a function of time R(t)  

      For forward approach :  

      For Reverse approach :

Hoping that in future I'll learn Graph theory , Social Network Analysis and add a dash of Game theory to spice it up , so that my friendship dynamics might take a giant leap into the future ,"To infinity and Beyond !"



"Every positive integer is one of Ramanujan's personal friends."
                           - John Littlewood (On hearing of the taxicab incident.)